Jody Nagel
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Voice-Leading Possibilities
Appendix 4

 
 

This Document is formatted for a 12-point font size.
 
 
     Appendix 4.
 
N = number of instruments (0 - 12) playing two N-note chords: "1st" and "2nd."
K = number of potential common-tones between the two chords.
D = held common-tones.
U = (K-D) = unheld common-tones.
B = (C1)(N-D)! - (C2)(N-D-1)! + (C3)(N-D-2)! ± . . .

     There will be K-D+1 terms. The Coefficients, Cx, are determined by the (K-D)th line of "Pascal's Triangle."
     The operations of subtraction and addition alternate between successive terms.
     If D=K=0, then B = N!
X = possible pitch-class-assignment permutations.
     X = [ ( N! / (N-D)! ) ] x [ ( K! / ( D! x (K-D)! ) ) ] x (N-D)! x B = (N! x K! x B) / (D! x U!)
     If D=K=0, then X = (N!)2
     If N=K=D, then X = N!
Y = possible pitch-class-assignment combinations.
     Y = (X / N!)
     If N=K=D, then Y = 1
     If D=K, then Y = B
     If D=0, then Y = B
     If D=K=0, then Y = B = N!, and Y is given in Bold-face.
     Note: B = Y2 for the case (N2 = N-D; K2 = K-D; D2 = D-D = 0). If D=0, then (N-D, K-D, 0) and the value of B are given in bold-face.
     Two Cases:
(1) common tones required to be held in the same octave.
(2) common tones are free either to be held at the same octave or to move up an octave or to move down an octave.
P1 & P2 = number of "Up-or-Down" options, for the two cases.     P1 = 2(N-D)
;     P2 = 2(N-D) x 3D.
If Y=X=0, then P1 & P2 are meaningless.
V1 & V2 = total voicings, for the two cases.     V1 = X x P1 ;     V2 = X x P2.
"Grand Total" = the number of voicings possible for a given N and K, for the two cases.


N = 0
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
- - 0, 0, 0 0 1 0, 0, 0 1 1 1 1 1 1 1
              Grand Total for (N, K): 0, 0 1   1
N = 1
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B 1, 0, 0 0 1 1, 0, 0 1 1 1 2 2 2 2
              Grand Total for (N, K): 1, 0 2   2
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A A 1, 1, 0 1 1 1, 1, 0 0 0 0 (2) 0 (2) 0
A A 1, 1, 1 0 1 0, 0, 0 1 1 1 1 1 3 3
              Grand Total for (N, K): 1, 1 1   3
N = 2
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D 2, 0, 0 0 2 2, 0, 0 2 4 2 4 16 4 16
              Grand Total for (N, K): 2, 0 16   16
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B B C 2, 1, 0 1 2 2, 1, 0 1 2 1 4 8 4 8
A B B C 2, 1, 1 0 2 2, 1, 0 1 2 1 2 4 6 12
              Grand Total for (N, K): 2, 1 12   20
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B A B 2, 2, 0 2 2 2, 2, 0 1 2 1 4 8 4 8
A B A B 2, 2, 1 1 2 1, 1, 0 0 0 0 (2) 0 (6) 0
A B A B 2, 2, 2 0 2 0, 0, 0 1 2 1 1 2 9 18
              Grand Total for (N, K): 2, 2 10   26
N = 3
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F 3, 0, 0 0 6 3, 0, 0 6 36 6 8 288 8 288
              Grand Total for (N, K): 3, 0 288   288
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C C D E 3, 1, 0 1 6 3, 1, 0 4 24 4 8 192 8 192
A B C C D E 3, 1, 1 0 6 2, 0, 0 2 12 2 4 48 12 144
              Grand Total for (N, K): 3, 1 240   336
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C B C D 3, 2, 0 2 6 3, 2, 0 3 18 3 8 144 8 144
A B C B C D 3, 2, 1 1 6 2, 1, 0 1 12 2 4 48 12 144
A B C B C D 3, 2, 2 0 6 1, 0, 0 1 6 1 2 12 18 108
              Grand Total for (N, K): 3, 2 204   396
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C A B C 3, 3, 0 3 6 3, 3, 0 2 12 2 8 96 8 96
A B C A B C 3, 3, 1 2 6 2, 2, 0 1 18 3 4 72 12 216
A B C A B C 3, 3, 2 1 6 1, 1, 0 0 0 0 (2) 0 (18) 0
A B C A B C 3, 3, 3 0 6 0, 0, 0 1 6 1 1 6 27 162
              Grand Total for (N, K): 3, 3 174   474
N = 4
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H 4, 0, 0 0 24 4, 0, 0 24 576 24 16 9,216 16 9,216
              Grand Total for (N, K): 4, 0 9,216   9,216
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D D E F G 4, 1, 0 1 24 4, 1, 0 18 432 18 16 6,912 16 6,912
A B C D D E F G 4, 1, 1 0 24 3, 0, 0 6 144 6 8 1,152 24 3,456
              Grand Total for (N, K): 4, 1 8,064   10,368
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D C D E F 4, 2, 0 2 24 4, 2, 0 14 336 14 16 5,376 16 5,376
A B C D C D E F 4, 2, 1 1 24 3, 1, 0 4 192 8 8 1,536 24 4,608
A B C D C D E F 4, 2, 2 0 24 2, 0, 0 2 48 2 4 192 36 1,728
              Grand Total for (N, K): 4, 2 7,104   11,712
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D B C D E 4, 3, 0 3 24 4, 3, 0 11 264 11 16 4,224 16 4,224
A B C D B C D E 4, 3, 1 2 24 3, 2, 0 3 216 9 8 1,728 24 5,184
A B C D B C D E 4, 3, 2 1 24 2, 1, 0 1 72 3 4 288 36 2,592
A B C D B C D E 4, 3, 3 0 24 1, 0, 0 1 24 1 2 48 54 1,296
              Grand Total for (N, K): 4, 3 6,288   13,296
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D A B C D 4, 4, 0 4 24 4, 4, 0 9 216 9 16 3,456 16 3,456
A B C D A B C D 4, 4, 1 3 24 3, 3, 0 2 192 8 8 1,536 24 4,608
A B C D A B C D 4, 4, 2 2 24 2, 2, 0 1 144 6 4 576 36 5,184
A B C D A B C D 4, 4, 3 1 24 1, 1, 0 0 0 0 (2) 0 (54) 0
A B C D A B C D 4, 4, 4 0 24 1, 0, 0 1 24 1 1 24 81 1,944
              Grand Total for (N, K): 4, 4 5,592   15,192
N = 5
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J 5, 0, 0 0 120 5, 0, 0 120 14,400 120 32 460, 800 32 460, 800
              Grand Total for (N, K): 5, 0 460, 800   460, 800
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E E F G H I 5, 1, 0 1 120 5, 1, 0 96 11,520 96 32 368,640 32 368,640
A B C D E E F G H I 5, 1, 1 0 120 4, 0, 0 24 2,880 24 16 46,080 48 138,240
              Grand Total for (N, K): 5, 1 414,720   506,880
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E D E F G H 5, 2, 0 2 120 5, 2, 0 78 9,360 78 32 299,520 32 299,520
A B C D E D E F G H 5, 2, 1 1 120 4, 1, 0 18 4,320 36 16 69,120 48 207,360
A B C D E D E F G H 5, 2, 2 0 120 3, 0, 0 6 720 6 8 5,760 72 51,840
              Grand Total for (N, K): 5, 2 374,400   558,720
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E C D E F G 5, 3, 0 3 120 5, 3, 0 64 7,680 64 32 245,760 32 245,760
A B C D E C D E F G 5, 3, 1 2 120 4, 2, 0 14 5,040 42 16 80,640 48 241,920
A B C D E C D E F G 5, 3, 2 1 120 3, 1, 0 4 1,440 12 8 11,520 72 103,680
A B C D E C D E F G 5 3, 3 0 120 2, 0, 0 2 240 2 4 960 108 25,920
              Grand Total for (N, K): 4, 3 6,288   13,296
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E B C D E F 5, 4, 0 4 120 5, 4, 0 53 6,360 53 32 203,520 32 203,520
A B C D E B C D E F 5, 4, 1 3 120 4, 3, 0 11 15,280 44 16 84,480 48 253,440
A B C D E B C D E F 5, 4, 2 2 120 3, 2, 0 3 2,160 18 8 17,280 72 155,520
A B C D E B C D E F 5, 4, 3 1 120 2, 1, 0 1 480 4 4 1,920 108 51,840
A B C D E B C D E F 5, 4, 4 0 120 1, 0, 0 1 120 1 2 240 162 19,440
              Grand Total for (N, K): 5, 4 307,440   683,760
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E A B C D E 5, 5 0 5 120 5, 5, 0 44 5,280 44 32 168,960 32 168,960
A B C D E A B C D E 5, 5, 1 4 120 4, 4, 0 9 5,400 45 16 86,400 48 259,200
A B C D E A B C D E 5, 5, 2 3 120 3, 3, 0 2 2,400 20 8 19,200 72 172,800
A B C D E A B C D E 5, 5, 3 2 120 2, 2, 0 1 1,200 10 4 4,800 108 129,600
A B C D E A B C D E 5, 5, 4 1 120 1, 1, 0 0 0 0 (2) 0 (162) 0
A B C D E A B C D E 5, 5, 5 0 120 0, 0, 0 1 120 1 1 120 243 29,160
              Grand Total for (N, K): 5, 5 279,480   759,720
N = 6
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J K L 6, 0, 0 0 720 6, 0, 0 720 518,400 720 64 33,177,600 64 33,177,600
              Grand Total for (N, K): 6, 0 33,177,600   33,177,600
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F F G H I J K 6, 1, 0 1 720 6, 1, 0 600 432,000 600 64 27,648,000 64 27,648,000
A B C D E F F G H I J K 6, 1, 1 0 720 5, 0, 0 120 86,400 120 32 2,764,800 96 8,294,400
              Grand Total for (N, K): 6, 1 30,412,800   35,942,400
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F E F G H I J 6, 2, 0 2 720 6, 2, 0 504 362,800 504 64 23,224,320 64 23,224,320
A B C D E F E F G H I J 6, 2, 1 1 720 5, 1, 0 96 138,240 192 32 4,423,680 96 13,271,040
A B C D E F E F G H I J 6, 2, 2 0 720 4, 0, 0 24 17,280 24 16 276,480 144 2,488,320
              Grand Total for (N, K): 6, 2 27,924,480   38,983,680
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F D E F G H I 6, 3, 0 3 720 6, 3, 0 426 306,720 426 64 19,630,080 64 19,630,080
A B C D E F D E F G H I 6, 3, 1 2 720 5, 2, 0 78 168,480 234 32 5,391,360 96 16,174,080
A B C D E F D E F G H I 6, 3, 2 1 720 4, 1, 0 18 38,880 54 16 622,080 144 5,598,720
A B C D E F D E F G H I 6 3, 3 0 720 3, 0, 0 6 4,320 6 8 34,560 216 933,120
              Grand Total for (N, K): 6, 3 25,678,080   42,336,000
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F C D E F G H 6, 4, 0 4 720 6, 4, 0 362 260,640 362 64 16,680,960 64 16,680,960
A B C D E F C D E F G H 6, 4, 1 3 720 5, 3, 0 64 184,320 256 32 5,898,240 96 17,694,720
A B C D E F C D E F G H 6, 4, 2 2 720 4, 2, 0 14 60,480 84 16 967,680 144 8,709,120
A B C D E F C D E F G H 6, 4, 3 1 720 3, 1, 0 4 11,520 16 8 92,160 216 2,488,320
A B C D E F C D E F G H 6, 4, 4 0 720 2, 0, 0 2 1,440 2 4 5,760 324 466,560
              Grand Total for (N, K): 6, 4 23,644,800   46,039,680
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F B C D E F G 6, 5, 0 5 720 6, 5, 0 309 222,480 309 64 14,238,720 64 14,238,720
A B C D E F B C D E F G 6, 5, 1 4 720 5, 4, 0 53 190,800 265 32 6,105,600 96 18,316,800
A B C D E F B C D E F G 6, 5, 2 3 720 4, 3, 0 11 79,200 110 16 1,267,200 144 11,404,800
A B C D E F B C D E F G 6, 5, 3 2 720 3, 2, 0 3 21,600 30 8 172,800 216 4,665,600
A B C D E F B C D E F G 6, 5, 4 1 720 2, 1, 0 1 3,600 5 4 14,400 324 1,166,400
A B C D E F B C D E F G 6, 5, 5 0 720 1, 0, 0 1 720 1 2 1,440 486 349,920
              Grand Total for (N, K): 6, 5 21,800,160   50,142,240
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F A B C D E F 6, 6, 0 6 720 6, 6, 0 265 190,800 265 64 12,211,200 64 12,211,200
A B C D E F A B C D E F 6, 6, 1 5 720 5, 5, 0 44 190,080 264 32 6,082,560 96 18,247,680
A B C D E F A B C D E F 6, 6, 2 4 720 4, 4, 0 9 97,200 135 16 1,555,200 144 13,996,800
A B C D E F A B C D E F 6, 6, 3 3 720 3, 3, 0 2 28,800 40 8 230,400 216 6,220,800
A B C D E F A B C D E F 6, 6, 4 2 720 2, 2, 0 1 10,800 15 4 43,200 324 3,499,200
A B C D E F A B C D E F 6, 6, 5 1 720 1, 1, 0 0 0 0 (2) 0 (486) 0
A B C D E F A B C D E F 6, 6, 6 0 720 0, 0, 0 1 720 1 1 720 729 524,880
              Grand Total for (N, K): 6, 6 20,123,280   54,700,560
N = 7
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G F G H I J K L 7, 2, 0 2 5,040 7, 2, 0 3,720 18,748,800 3,720 128 2,399,846,400 128 2,399,846,400
A B C D E F G F G H I J K L 7, 2, 1 1 5,040 6, 1, 0 600 6,048,000 1,200 64 387,072,000 192 1,161,216,000
A B C D E F G F G H I J K L 7, 2, 2 0 5,040 5, 0, 0 120 604,800 120 32 19,353,600 288 174,182,400
              Grand Total for (N, K): 7, 2 2,806,272,000   3,735,244,800
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G E F G H I J K 7, 3, 0 3 5,040 7, 3, 0 3,216 16,208,640 3,216 128 2,074,705,920 128 2,074,705,920
A B C D E F G E F G H I J K 7, 3, 1 2 5,040 6, 2, 0 504 7,620,480 1,512 64 487,710,720 192 1,463,132,160
A B C D E F G E F G H I J K 7, 3, 2 1 5,040 5, 1, 0 96 1,451,520 288 32 46,448,640 288 418,037,760
A B C D E F G E F G H I J K 7 3, 3 0 5,040 4, 0, 0 24 120,960 24 16 1,935,360 432 52,254,720
              Grand Total for (N, K): 7, 3 2,610,800,640   4,008,130,560
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G D E F G H I J 7, 4, 0 4 5,040 7, 4, 0 2,790 14,061,600 2,790 128 1,799,884,800 128 1,799,884,800
A B C D E F G D E F G H I J 7, 4, 1 3 5,040 6, 3, 0 426 8,588,160 1,704 64 549,642,240 192 1,648,926,720
A B C D E F G D E F G H I J 7, 4, 2 2 5,040 5, 2, 0 78 2,358,720 468 32 75,479,040 288 679,311,360
A B C D E F G D E F G H I J 7, 4, 3 1 5,040 4, 1, 0 18 362,880 72 16 5,806,080 432 156,764,160
A B C D E F G D E F G H I J 7, 4, 4 0 5,040 3, 0, 0 6 30,240 6 8 241,920 648 19,595,520
              Grand Total for (N, K): 7, 4 2,431,054,080   4,304,482,560
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G C D E F G H I 7, 5, 0 5 5,040 7, 5, 0 2,428 12,237,120 2,428 128 1,566,351,360 128 1,566,351,360
A B C D E F G C D E F G H I 7, 5, 1 4 5,040 6, 4, 0 362 9,122,400 1,810 64 583,833,600 192 1,751,500,800
A B C D E F G C D E F G H I 7, 5, 2 3 5,040 5, 3, 0 64 3,225,600 640 32 103,219,200 288 928,972,800
A B C D E F G C D E F G H I 7, 5, 3 2 5,040 4, 2, 0 14 705,600 140 16 11,289,600 432 304,819,200
A B C D E F G C D E F G H I 7, 5, 4 1 5,040 3, 1, 0 4 100,800 20 8 806,400 648 65,318,400
A B C D E F G C D E F G H I 7, 5, 5 0 5,040 2, 0, 0 2 10,080 2 4 40,320 972 9,797,760
              Grand Total for (N, K): 7, 5 2,265,540,480   4,626,760,320
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G B C D E F G H 7, 6, 0 6 5,040 7, 6, 0 2,119 10,679,760 2,119 128 1,367,009,280 128 1,367,009,280
A B C D E F G B C D E F G H 7, 6, 1 5 5,040 6, 5, 0 309 9,344,160 1,854 64 598,026,240 192 1,794,078,720
A B C D E F G B C D E F G H 7, 6, 2 4 5,040 5, 4, 0 53 4,006,800 795 32 128,217,600 288 1,153,958,400
A B C D E F G B C D E F G H 7, 6, 3 3 5,040 4, 3, 0 11 1,108,800 220 16 17,740,800 432 479,001,600
A B C D E F G B C D E F G H 7, 6, 4 2 5,040 3, 2, 0 3 226,800 45 8 1,814,400 648 146,966,400
A B C D E F G B C D E F G H 7, 6, 5 1 5,040 2, 1, 0 1 30,240 6 4 120,960 972 29,393,280
A B C D E F G B C D E F G H 7, 6, 6 0 5,040 1, 0, 0 1 5,040 1 2 10,080 1,458 7,348,320
              Grand Total for (N, K): 7, 6 2,112,939,360   4,977,756,000
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G A B C D E F G 7, 7, 0 7 5,040 7, 7, 0 1,854 9,344,160 1,854 128 1,196,052,480 128 1,196,052,480
A B C D E F G A B C D E F G 7, 7, 1 6 5,040 6, 6, 0 265 9,349,200 1,855 64 598,348,800 192 1,795,046,400
A B C D E F G A B C D E F G 7, 7, 2 5 5,040 5, 5, 0 44 4,656,960 924 32 149,022,720 288 1,341,204,480
A B C D E F G A B C D E F G 7, 7, 3 4 5,040 4, 4, 0 9 1,587,600 315 16 25,401,600 432 685,843,200
A B C D E F G A B C D E F G 7, 7, 4 3 5,040 3, 3, 0 2 352,800 70 8 2,822,400 648 228,614,400
A B C D E F G A B C D E F G 7, 7, 5 2 5,040 2, 2, 0 1 105,840 21 4 423,360 972 102,876,480
A B C D E F G A B C D E F G 7, 7, 6 1 5,040 1, 1, 0 0 0 0 (2) 0 (1,458) 0
A B C D E F G A B C D E F G 7, 7, 7 0 5,040 0, 0, 0 1 5,040 1 1 5,040 2,187 11,022,480
              Grand Total for (N, K): 7, 7 1,972,076,400   5,360,659,920
N = 8
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H E F G H I J K L 8, 4, 0 4 40,320 8, 4, 0 24,024 968,647,680 24,024 256 247,973,806,080 256 247,973,806,080
A B C D E F G H E F G H I J K L 8, 4, 1 3 40,320 7, 3, 0 3,216 518,676,480 12,864 128 66,390,589,440 384 199,171,768,320
A B C D E F G H E F G H I J K L 8, 4, 2 2 40,320 6, 2, 0 504 121,927,680 3,024 64 7,803,371,520 576 70,230,343,680
A B C D E F G H E F G H I J K L 8, 4, 3 1 40,320 5, 1, 0 96 15,482,880 384 32 495,452,160 864 13,377,208,320
A B C D E F G H E F G H I J K L 8, 4, 4 0 40,320 4, 0, 0 24 967,680 24 16 15,482,880 1,296 1,254,113,280
              Grand Total for (N, K): 8, 4 322,678,702,080   532,007,239,680
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H D E F G H I J K 8, 5, 0 5 40,320 8, 5, 0 21,234 856,154,880 21,234 256 219,175,649,280 256 219,175,649,280
A B C D E F G H D E F G H I J K 8, 5, 1 4 40,320 7, 4, 0 2,790 562,464,000 13,950 128 71,995,392,000 384 215,986,176,000
A B C D E F G H D E F G H I J K 8, 5, 2 3 40,320 6, 3, 0 426 171,763,200 4,260 64 10,992,844,800 576 98,935,603,200
A B C D E F G H D E F G H I J K 8, 5, 3 2 40,320 5, 2, 0 78 31,449,600 780 32 1,006,387,200 864 27,172,454,400
A B C D E F G H D E F G H I J K 8, 5, 4 1 40,320 4, 1, 0 18 3,628,800 90 16 58,060,800 1,296 4,702,924,800
A B C D E F G H D E F G H I J K 8, 5, 5 0 40,320 3, 0, 0 6 241,920 6 8 1,935,360 1,944 470,292,480
              Grand Total for (N, K): 8, 5 303,230,269,440   566,443,100,160
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H C D E F G H I J 8, 6, 0 6 40,320 8, 6, 0 18,806 758,257,920 18,806 256 194,114,027,520 256 194,114,027,520
A B C D E F G H C D E F G H I J 8, 6, 1 5 40,320 7, 5, 0 2,428 587,381,760 14,568 128 75,184,865,280 384 225,554,595,840
A B C D E F G H C D E F G H I J 8, 6, 2 4 40,320 6, 4, 0 362 218,937,600 5,430 64 14,012,006,400 576 126,108,057,600
A B C D E F G H C D E F G H I J 8, 6, 3 3 40,320 5, 3, 0 64 51,609,600 1,280 32 1,651,507,200 864 44,590,694,400
A B C D E F G H C D E F G H I J 8, 6, 4 2 40,320 4, 2, 0 8 8,467,200 210 16 135,475,200 1,296 10,973,491,200
A B C D E F G H C D E F G H I J 8, 6, 5 1 40,320 3, 1, 0 4 967,680 24 8 7,741,440 1,944 1,881,169,920
A B C D E F G H C D E F G H I J 8, 6, 6 0 40,320 2, 0, 0 2 80,640 2 4 322,560 2,916 235,146,240
              Grand Total for (N, K): 8, 6 285,105,945,600   603,457,182,720
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H B C D E F G H I 8, 7, 0 7 40,320 8, 7, 0 16,687 672,819,840 16,687 256 172,241,879,040 256 172,241,879,040
A B C D E F G H B C D E F G H I 8, 7, 1 6 40,320 7, 6, 0 2,119 598,066,560 14,833 128 76,552,519,680 384 229,657,559,040
A B C D E F G H B C D E F G H I 8, 7, 2 5 40,320 6, 5, 0 309 261,636,480 6,489 64 16,744,734,720 576 150,702,612,480
A B C D E F G H B C D E F G H I 8, 7, 3 4 40,320 5, 4, 0 53 74,793,600 1,855 32 2,393,395,200 864 64,621,670,400
A B C D E F G H B C D E F G H I 8, 7, 4 3 40,320 4, 3, 0 11 15,523,200 385 16 248,371,200 1,296 20,118,067,200
A B C D E F G H B C D E F G H I 8, 7, 5 2 40,320 3, 2, 0 3 2,540,160 63 8 20,321,280 1,944 4,938,071,040
A B C D E F G H B C D E F G H I 8, 7, 6 1 40,320 2, 1, 0 1 82,240 7 4 1,128,960 2,916 823,011,840
A B C D E F G H B C D E F G H I 8, 7, 7 0 40,320 1, 0, 0 1 40,320 1 2 80,640 4,374 176,359,680
              Grand Total for (N, K): 8, 7 268,202,430,720   643,279,230,720
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H A B C D E F G H 8, 8, 0 8 40,320 8, 8, 0 14,833 598,066,560 14,833 256 153,105,039,360 256 153,105,039,360
A B C D E F G H A B C D E F G H 8, 8, 1 7 40,320 7, 7, 0 1,854 598,026,240 14,832 128 76,547,358,720 384 229,642,076,160
A B C D E F G H A B C D E F G H 8, 8, 2 6 40,320 6, 6, 0 265 299,174,400 7,420 64 19,147,161,600 576 172,324,454,400
A B C D E F G H A B C D E F G H 8, 8, 3 5 40,320 5, 5, 0 44 99,348,480 2,464 32 3,179,151,360 864 85,837,086,720
A B C D E F G H A B C D E F G H 8, 8, 4 4 40,320 4, 4, 0 9 25,401,600 630 16 406,425,600 1,296 32,920,473,600
A B C D E F G H A B C D E F G H 8, 8, 5 3 40,320 3, 3, 0 2 4,515,840 112 8 36,126,720 1,944 8,778,792,960
A B C D E F G H A B C D E F G H 8, 8, 6 2 40,320 2, 2, 0 1 1,128,960 28 4 4,515,840 2,916 3,292,047,360
A B C D E F G H A B C D E F G H 8, 8, 7 1 40,320 1, 1, 0 0 0 0 (2) 0 (4,374) 0
A B C D E F G H A B C D E F G H 8, 8, 8 0 40,320 0, 0, 0 1 40,320 1 1 40,320 6,561 264,539,520
              Grand Total for (N, K): 8, 8 252,425,819,520   686,164,510,080
N = 9
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I D E F G H I J K L 9, 6, 0 6 362,880 9, 6, 0 183,822 66,705,327,360 183,822 512 34,153,127,608,320 512 34,153,127,608,320
A B C D E F G H I D E F G H I J K L 9, 6, 1 5 362,880 8, 5, 0 21,234 46,232,363,520 127,404 256 11,835,485,061,120 768 35,506,455,183,360
A B C D E F G H I D E F G H I J K L 9, 6, 2 4 362,880 7, 4, 0 2,790 15,186,528,00 41,850 128 1,943,875,584,000 1,152 17,494,880,256,000
A B C D E F G H I D E F G H I J K L 9, 6, 3 3 362,880 6, 3, 0 426 3,091,737,600 8,520 64 197,871,206,400 1,728 5,342,522,572,800
A B C D E F G H I D E F G H I J K L 9, 6, 4 2 362,880 5, 2, 0 78 424,569,600 1,170 32 13,586,227,200 2,592 1,100,484,403,200
A B C D E F G H I D E F G H I J K L 9, 6, 5 1 362,880 4, 1, 0 8 39,191,040 108 16 627,056,640 3,888 152,374,763,520
A B C D E F G H I D E F G H I J K L 9, 6, 6 0 362,880 3, 0, 0 6 2,177,280 6 8 17,418,240 5,832 12,697,896,960
              Grand Total for (N, K): 9, 6 48,144,590,161,920   93,762,542,684,160
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I C D E F G H I J K 9, 7, 0 7 362,880 9, 7, 0 165,016 59,881,006,080 165,016 512 30,659,075,112,960 512 30,659,075,112,960
A B C D E F G H I C D E F G H I J K 9, 7, 1 6 362,880 8, 6, 0 18,806 47,770,248,960 131,642 256 12,229,183,733,760 768 36,687,551,201,280
A B C D E F G H I C D E F G H I J K 9, 7, 2 5 362,880 7, 5, 0 2,428 18,502,525,440 50,988 128 2,368,323,256,320 1,152 21,314,909,306,880
A B C D E F G H I C D E F G H I J K 9, 7, 3 4 362,880 6, 4, 0 362 4,597,689,600 12,670 64 294,252,134,400 1,728 7,944,807,628,800
A B C D E F G H I C D E F G H I J K 9, 7, 4 3 362,880 5, 3, 0 64 812,851,200 2,240 32 26,011,238,400 2,592 2,106,910,310,400
A B C D E F G H I C D E F G H I J K 9, 7, 5 2 362,880 4, 2, 0 14 106,686,720 294 16 1,706,987,520 3,888 414,797,967,360
A B C D E F G H I C D E F G H I J K 9, 7, 6 1 362,880 3, 1, 0 4 10,160,640 28 8 81,285,120 5,832 59,256,852,480
A B C D E F G H I C D E F G H I J K 9, 7, 7 0 362,880 2, 0, 0 2 725,760 2 4 2,903,040 8,748 6,348,948,480
              Grand Total for (N, K): 9, 7 45,578,636,651,520   99,193,657,328,640
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I B C D E F G H I J 9, 8, 0 8 362,880 9, 8, 0 148,329 53,825,627,520 148,329 512 27,558,721,290,240 512 27,558,721,290,240
A B C D E F G H I B C D E F G H I J 9, 8, 1 7 362,880 8, 7, 0 16,687 48,443,028,480 133,496 256 12,401,415,290,880 768 37,204,245,872,640
A B C D E F G H I B C D E F G H I J 9, 8, 2 6 362,880 7, 6, 0 2,119 21,530,396,160 59,332 128 2,755,890,708,480 1,152 24,803,016,376,320
A B C D E F G H I B C D E F G H I J 9, 8, 3 5 362,880 6, 5, 0 309 6,279,275,520 17,304 64 401,873,633,280 1,728 10,850,588,098,560
A B C D E F G H I B C D E F G H I J 9, 8, 4 4 362,880 5, 4, 0 53 1,346,284,800 3,710 32 43,081,113,600 2,592 3,489,570,201,600
A B C D E F G H I B C D E F G H I J 9, 8, 5 3 362,880 4, 3, 0 11 223,534,080 616 16 3,576,545,280 3,888 869,100,503,040
A B C D E F G H I B C D E F G H I J 9, 8, 6 2 362,880 3, 2, 0 3 30,481,920 84 8 243,855,360 5,832 177,770,557,440
A B C D E F G H I B C D E F G H I J 9, 8, 7 1 362,880 2, 1, 0 1 2,903,040 8 4 11,612,160 8,748 25,395,793,920
A B C D E F G H I B C D E F G H I J 9, 8, 8 0 362,880 1, 0, 0 1 362,880 1 2 725,760 13,122 4,761,711,360
              Grand Total for (N, K): 9, 8 43,164,814,775,040   104,983,170,405,120
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I A B C D E F G H I 9, 9, 0 9 362,880 9, 9, 0 133,496 48,443,028,480 133,496 512 24,802,830,581,760 512 24,802,830,581,760
A B C D E F G H I A B C D E F G H I 9, 9, 1 8 362,880 8, 8, 0 14,833 48,443,391,360 133,497 256 12,401,508,188,160 768 37,204,524,564,480
A B C D E F G H I A B C D E F G H I 9, 9, 2 7 362,880 7, 7, 0 1,854 24,220,062,720 66,744 128 3,100,168,028,160 1,152 27,901,512,253,440
A B C D E F G H I A B C D E F G H I 9, 9, 3 6 362,880 6, 6, 0 265 8,077,708,800 22,260 64 516,973,363,200 1,728 13,958,280,806,4000
A B C D E F G H I A B C D E F G H I 9, 9, 4 5 362,880 5, 5, 0 44 2,011,806,720 5,544 32 64,377,815,040 2,592 5,214,603,018,240
A B C D E F G H I A B C D E F G H I 9, 9, 5 4 362,880 4, 4, 0 9 411,505,920 1,134 16 6,584,094,720 3,888 1,599,935,016,960
A B C D E F G H I A B C D E F G H I 9, 9, 6 3 362,880 3, 3, 0 2 60,963,840 168 8 487,710,720 5,832 355,541,114,880
A B C D E F G H I A B C D E F G H I 9, 9, 7 2 362,880 2, 2, 0 1 13,063,680 36 4 52,254,720 8,748 114,281,072,640
A B C D E F G H I A B C D E F G H I 9, 9, 8 1 362,880 1, 1, 0 0 0 0 (2) 0 (13,122) 0
A B C D E F G H I A B C D E F G H I 9, 9, 9 0 362,880 0, 0, 0 1 362,880 1 1 362,880 19,683 7,142,567,040
              Grand Total for (N, K): 9, 9 40,892,982,399,360   111,158,650,995,840
N = 10
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J C D E F G H I J K L 10, 8, 0 8 3,628,800 10, 8, 0 1,616,786 5,866,993,036,800 1,616,786 1,024 6,007,800,869,683,200 1,024 6,007,800,869,683,200
A B C D E F G H I J C D E F G H I J K L 10, 8, 1 7 3,628,800 9, 7, 0 165,016 4,790,480,486,400 1,320,128 512 2,452,726,009,036,800 1,536 7,358,178,027,110,400
A B C D E F G H I J C D E F G H I J K L 10, 8, 2 6 3,628,800 8, 6, 0 18,806 1,910,809,958,400 526,568 256 489,167,349,350,400 2,304 4,402,506,144,153,600
A B C D E F G H I J C D E F G H I J K L 10, 8, 3 5 3,628,800 7, 5, 0 2,428 493,400,678,400 135,968 128 63,155,286,835,200 3,456 1,705,192,744,550,400
A B C D E F G H I J C D E F G H I J K L 10, 8, 4 4 3,628,800 6, 4, 0 362 91,953,792,000 25,340 64 5,885,042,688,000 5,184 476,688,457,728,000
A B C D E F G H I J C D E F G H I J K L 10, 8, 5 3 3,628,800 5, 3, 0 64 13,005,619,200 3,584 32 416,179,814,400 7,776 101,131,694,899,200
A B C D E F G H I J C D E F G H I J K L 10, 8, 6 2 3,628,800 4, 2, 0 14 1,422,489,600 392 16 22,759,833,600 11,664 16,591,918,694,400
A B C D E F G H I J C D E F G H I J K L 10, 8, 7 1 3,628,800 3, 1, 0 4 116,121,600 32 8 928,972,800 17,496 2,031,663,513,600
A B C D E F G H I J C D E F G H I J K L 10, 8, 8 0 3,628,800 2, 0, 0 2 7,257,600 2 4 29,030,400 26,244 190,468,454,400
              Grand Total for (N, K): 10, 8 9,019,174,455,244,800   20,070,311,988,787,200
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J B C D E F G H I J K 10, 9, 0 9 3,628,800 10, 9, 0 1,468,457 5,328,736,761,600 1,468,457 1,024 5,456,626,443,878,400 1,024 5,456,626,443,878,400
A B C D E F G H I J B C D E F G H I J K 10, 9, 1 8 3,628,800 9, 8, 0 148,329 4,844,306,476,800 1,334,961 512 2,480,284,916,121,600 1,536 7,440,854,748,364,800
A B C D E F G H I J B C D E F G H I J K 10, 9, 2 7 3,628,800 8, 7, 0 16,687 2,179,936,281,600 600,732 256 558,063,688,089,600 2,304 5,022,573,192,806,400
A B C D E F G H I J B C D E F G H I J K 10, 9, 3 6 3,628,800 7, 6, 0 2,119 645,911,884,800 177,996 128 82,676,721,254,400 3,456 2,232,271,473,868,800
A B C D E F G H I J B C D E F G H I J K 10, 9, 4 5 3,628,800 6, 5, 0 309 141,283,699,200 38,934 64 9,042,156,748,800 5,184 732,414,696,652,800
A B C D E F G H I J B C D E F G H I J K 10, 9, 5 4 3,628,800 5, 4, 0 53 24,233,126,400 6,678 32 775,460,044,800 7,776 188,436,790,886,400
A B C D E F G H I J B C D E F G H I J K 10, 9, 6 3 3,628,800 4, 3, 0 11 3,353,011,200 924 16 53,648,179,200 11,664 39,109,522,636,800
A B C D E F G H I J B C D E F G H I J K 10, 9, 7 2 3,628,800 3, 2, 0 3 391,910,400 108 8 3,135,283,200 17,496 6,856,864,358,400
A B C D E F G H I J B C D E F G H I J K 10, 9, 8 1 3,628,800 2, 1, 0 1 32,659,200 9 4 130,636,800 26,244 857,108,044,800
A B C D E F G H I J B C D E F G H I J K 10, 9, 9 0 3,628,800 1, 0, 0 1 3,628,800 1 2 7,257,600 39,366 142,851,340,800
              Grand Total for (N, K): 10, 9 8,587,526,307,494,400   21,120,143,692,838,400
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J A B C D E F G H I J 10, 10, 0 10 3,628,800 10, 10, 0 1,334,961 4,844,306,476,800 1,334,961 1,024 4,960,569,832,243,200 1,024 4,960,569,832,243,200
A B C D E F G H I J A B C D E F G H I J 10, 10, 1 9 3,628,800 9, 9, 0 133,496 4,844,302,848,000 1,334,960 512 2,480,283,058,176,000 1,536 7,440,849,174,528,000
A B C D E F G H I J A B C D E F G H I J 10, 10, 2 8 3,628,800 8, 8, 0 14,833 2,422,169,568,000 667,485 256 620,075,409,408,000 2,304 5,580,678,684,672,000
A B C D E F G H I J A B C D E F G H I J 10, 10, 3 7 3,628,800 7, 7, 0 1,854 807,335,424,000 222,480 128 103,338,934,272,000 3,456 2,790,151,225,344,000
A B C D E F G H I J A B C D E F G H I J 10, 10, 4 6 3,628,800 6, 6, 0 265 201,942,720,000 55,650 64 12,924,334,080,000 5,184 1,046,871,060,480,000
A B C D E F G H I J A B C D E F G H I J 10, 10, 5 5 3,628,800 5, 5, 0 44 40,236,134,400 11,088 32 1,287,556,300,800 7,776 312,876,181,094,400
A B C D E F G H I J A B C D E F G H I J 10, 10, 6 4 3,628,800 4, 4, 0 9 6,858,432,000 1,890 16 109,734,912,000 11,664 79,996,750,848,000
A B C D E F G H I J A B C D E F G H I J 10, 10, 7 3 3,628,800 3, 3, 0 2 870,912,000 240 8 6,967,296,000 17,496 15,237,476,352,000
A B C D E F G H I J A B C D E F G H I J 10, 10, 8 2 3,628,800 2, 2, 0 1 163,296,000 45 4 653,184,000 26,244 4,285,540,224,000
A B C D E F G H I J A B C D E F G H I J 10, 10, 9 1 3,628,800 1, 1, 0 0 0 0 (2) 0 (39,366) 0
A B C D E F G H I J A B C D E F G H I J 10, 10, 10 0 3,628,800 0, 0, 0 1 3,628,800 1 1 3,628,800 59,049 214,277,011,200
              Grand Total for (N, K): 10, 10 8,178,596,483,500,800   22,231,730,202,796,800
N = 11
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 0 10 39,916,800 11, 10, 0 16,019,531 639,448,415,020,800 16,019,531 2,048 1,309,590,353,962,598,400 2,048 1,309,590,353,962,598,400
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 1 9 39,916,800 10, 9, 0 1,468,457 586,161,043,776,000 14,684,570 1,024 600,228,908,826,624,000 3,072 1,800,686,726,479,872,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 2 8 39,916,800 9, 8, 0 148,329 266,436,856,224,000 6,674,805 512 136,415,670,386,688,000 4,608 1,227,741,033,480,192,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 3 7 39,916,800 8, 7, 0 16,687 79,930,996,992,000 2,002,440 256 20,462,335,229,952,000 6,912 552,483,051,208,704,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 4 6 39,916,800 7, 6, 0 2,119 17,762,576,832,000 444,990 128 2,273,609,834,496,000 10,368 184,162,396,594,176,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 5 5 39,916,800 6, 5, 0 309 3,108,241,382,400 77,868 64 198,927,448,473,600 15,552 48,339,369,979,084,800
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 6 4 39,916,800 5, 4, 0 53 444,273,984,000 11,130 32 14,216,767,488,000 23,328 10,364,023,498,752,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 7 3 39,916,800 4, 3, 0 11 52,690,176,000 1,320 16 843,042,816,000 34,992 1,843,734,638,592,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 8 2 39,916,800 3, 2, 0 3 5,388,768,000 135 8 43,110,144,000 52,488 282,845,654,784,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 9 1 39,916,800 2, 1, 0 1 399,168,000 10 4 1,596,672,000 78,732 31,427,294,976,000
A B C D E F G H I J K B C D E F G H I J K L 11, 10, 10 0 39,916,800 1, 0, 0 1 39,916,800 1 2 79,833,600 118,098 4,714,094,246,400
              Grand Total for (N, K): 11, 10 2,069,184,910,285,785,600   5,135,529,676,885,977,600
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 0 11 39,916,800 11, 11, 0 14,684,570 586,161,043,776,000 14,684,570 2,048 1,200,457,817,653,248,000 2,048 1,200,457,817,653,248,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 1 10 39,916,800 10, 10, 0 1,334,961 586,161,083,792,800 14,684,571 1,024 600,228,949,803,827,200 3,072 1,800,686,849,411,481,600
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 2 9 39,916,800 9, 9, 0 133,496 293,080,322,304,000 7,342,280 512 150,057,125,019,648,000 4,608 1,350,514,125,176,832,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 3 8 39,916,800 8, 8, 0 14,833 97,694,172,576,000 2,447,445 256 25,009,708,179,456,000 6,912 675,262,120,845,312,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 4 7 39,916,800 7, 7, 0 1,854 24,421,896,576,000 611,820 128 3,126,002,761,728,000 10,368 253,206,223,699,968,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 5 6 39,916,800 6, 6, 0 265 4,887,013,824,000 122,430 64 312,768,884,736,000 15,552 76,002,838,990,848,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 6 5 39,916,800 5, 5, 0 44 811,428,710,400 20,328 32 25,965,718,732,800 23,328 18,929,008,956,211,200
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 7 4 39,916,800 4, 4, 0 9 118,552,896,000 2,970 16 1,896,846,336,000 34,992 4,148,402,936,832,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 8 3 39,916,800 3, 3, 0 2 13,172,544,000 330 8 105,380,352,000 52,488 691,400,489,472,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 9 1 39,916,800 2, 2, 0 1 2,195,424,000 55 4 8,781,696,000 78,732 172,850,122,368,000
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 10 1 39,916,800 1, 1, 0 0 0 0 (2) 0 (118,098) 0
A B C D E F G H I J K A B C D E F G H I J K 11, 11, 11 0 39,916,800 0, 0, 0 1 39,916,800 1 1 39,916,800 177,147 7,071,141,369,600
              Grand Total for (N, K): 11, 11 1,979,220,349,069,676,800   5,380,078,709,423,942,400
N = 12
1st chord 2nd chord N, K, D U N! N-D,   K-D,   0 B X Y P1 V1 P2 V2
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 0 12 479,001,600 12, 12, 0 176,214,841 84,407,190,782,745,600 176,214,841 4,096 345,731,853,446,125,977,600 4,096 345,731,853,446,125,977,600
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 1 11 479,001,600 11, 11, 0 14,684,570 84,407,190,303,744,000 176,214,840 2,048 172,865,925,742,067,712,000 6,144 518,597,777,226,203,136,000
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 2 10 479,001,600 10, 10, 0 1,334,961 42,203,598,025,881,600 88,107,426 1,024 43,216,484,378,502,758,400 9,216 388,948,359,406,524,825,600
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 3 9 479,001,600 9, 9, 0 133,496 14,067,855,470,592,000 29,369,120 512 7,202,742,000,943,104,000 13,824 194,474,034,025,463,808,000
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 4 8 479,001,600 8, 8, 0 14,833 3,516,990,212,736,000 7,342,335 256 900,349,494,460,416,000 20,736 72,928,309,051,293,696,000
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 5 7 479,001,600 7, 7, 0 1,854 703,350,621,388,800 1,468,368 128 90,028,879,537,766,400 31,104 21,877,017,727,677,235,200
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 6 6 479,001,600 6, 6, 0 265 117,288,331,776,000 244,860 64 7,506,453,233,664,000 46,656 5,472,204,407,341,056,000
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 7 5 479,001,600 5, 5, 0 44 16,692,247,756,800 34,848 32 534,151,928,217,600 69,984 1,168,190,267,011,891,200
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 8 4 479,001,600 4, 4, 0 9 2,133,952,128,000 4,455 16 34,143,234,048,000 104,976 224,013,758,588,928,000
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 9 3 479,001,600 3, 3, 0 2 210,760,704,000 440 8 1,686,085,632,000 157,464 33,187,223,494,656,000
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 10 2 479,001,600 2, 2, 0 1 31,614,105,600 66 4 126,456,422,400 236,196 7,467,125,286,297,600
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 11 1 479,001,600 1, 1, 0 0 0 0 (2) 0 (354,294) 0
A B C D E F G H I J K L A B C D E F G H I J K L 12, 12, 12 0 479,001,600 0, 0, 0 1 479,001,600 1 1 479,001,600 531,441 254,561,089,305,600
              Grand Total for (N, K): 12, 12 570,015,460,503,054,720,000   1,549,462,668,226,094,812,800

 
 
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