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A187239
Number of ways to place 7 nonattacking bishops on an n X n board.
6
0, 0, 0, 0, 440, 38368, 1022320, 14082528, 126490352, 837543200, 4412818240, 19447224864, 74255991784, 251997948736, 774861621936, 2191005028672, 5764306674400, 14243327787456, 33309659739904, 74194554880960, 158241369977880, 324605935279648, 642894402918768
OFFSET
1,5
LINKS
Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016
E. Weisstein, Bishops Problem, mathWorld.
Index entries for linear recurrences with constant coefficients, signature (6, -6, -34, 84, 42, -322, 162, 603, -708, -540, 1260, 0, -1260, 540, 708, -603, -162, 322, -42, -84, 34, 6, -6, 1).
FORMULA
a(n) = n^14/5040 - n^13/180 + 313n^12/4320 - 383n^11/648 + 14797n^10/4320 - 38233n^9/2520 + 3217n^8/60 - 145469n^7/945 + 1546679n^6/4320 - 4297801n^5/6480 + 257903n^4/270 - 3915679n^3/3780 + 1787007n^2/2240 - 318023n/840 + 9503/128 + (-n^8/192 + n^7/8 - 389n^6/288 + 689n^5/80 - 319n^4/9 + 1153n^3/12 - 95965n^2/576 + 20129n/120 - 9503/128)*(-1)^n.
G.f.: -8x^5*(630x^18 + 10620x^17 + 153525x^16 + 1211058x^15 + 6621390x^14 + 24647178x^13 + 66958554x^12 + 133891418x^11 + 202680754x^10 + 232634698x^9 + 204008900x^8 + 135332502x^7 + 67245306x^6 + 24326718x^5 + 6174582x^4 + 1024222x^3 + 99344x^2 + 4466x + 55)/((x-1)^15*(x+1)^9).
a(7) = A002465(7).
MATHEMATICA
CoefficientList[Series[- 8 x^4 (630 x^18 + 10620 x^17 + 153525 x^16 + 1211058 x^15 + 6621390 x^14 + 24647178 x^13 + 66958554 x^12 + 133891418 x^11 + 202680754 x^10 + 232634698 x^9 + 204008900 x^8 + 135332502 x^7 + 67245306 x^6 + 24326718 x^5 + 6174582 x^4 + 1024222 x^3 + 99344 x^2 + 4466 x + 55) / ((x - 1)^15 (x + 1)^9), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 02 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Mar 07 2011
STATUS
approved