A187242 Number of ways to place 10 nonattacking bishops on an n X n board.

0, 0, 0, 0, 0, 64, 81184, 12448832, 627961728, 15915225216, 251806066272, 2814607288320, 24088436720256, 166645918174848, 969258913391552, 4878776675787392, 21731689658569984, 87161301448676352, 319192073724720448, 1079363369445639936, 3401826465353378560, 10070308904424957632, 28183638842590122720

Offset

1,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016

V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)

Index entries for linear recurrences with constant coefficients, signature (6, 0, -70, 105, 336, -896, -720, 3900, -280, -10752, 6552, 20020, -21840, -24960, 43472, 18018, -60060, 0, 60060, -18018, -43472, 24960, 21840, -20020, -6552, 10752, 280, -3900, 720, 896, -336, -105, 70, 0, -6, 1).

Formula

a(n) = n^20/3628800 - n^19/60480 + 341n^18/725760 - 45949n^17/5443200 + 235433n^16/2177280 - 308291n^15/291600 + 14982871n^14/1814400 - 43484267n^13/816480 + 175706737n^12/604800 - 2444962049n^11/1796256 + 30003106793n^10/5443200 - 44899907477n^9/2332800 + 9919713547n^8/172800 - 18390588424n^7/127575 + 217346831209n^6/725760 - 8233418533709n^5/16329600 + 104224385179n^4/155520 - 14600765627n^3/21600 + 583132621007n^2/1209600 - 46669993739n/221760 + 19990663/512 + (-n^14/40320 + n^13/720 - 1267n^12/34560 + 15721n^11/25920 - 730663n^10/103680 + 5532407n^9/90720 - 98193341n^8/241920 + 10640393n^7/5040 - 99209431n^6/11520 + 1417368727n^5/51840 - 686809973n^4/10368 + 2144839679n^3/18144 - 1683044471n^2/11520 + 2242597633n/20160 - 19990663/512)*(-1)^n.

G.f.: -32x^6*(113400x^29 + 2518560x^28 + 55426428x^27 + 713122128x^26 + 7133734665x^25 + 51575533686x^24 + 289157705424x^23 + 1253334719652x^22 + 4339842816598x^21 + 12089938835312x^20 + 27595185140132x^19 + 51899069651452x^18 + 81237872407883x^17 + 106097483667238x^16 + 116126611566624x^15 + 106417824457960x^14 + 81632991696988x^13 + 52161861060464x^12 + 27621327391332x^11 + 11998025297736x^10 + 4224689442543x^9 + 1183463783138x^8 + 257650398544x^7 + 42074808244x^6 + 4911799606x^5 + 379785344x^4 + 17289788x^3 + 373804x^2 + 2525x + 2)/((x-1)^21*(x+1)^15).

a(10) = A002465(10).

Mathematica

CoefficientList[Series[- 32 x^5 (113400 x^29 + 2518560 x^28 + 55426428 x^27 + 713122128 x^26 + 7133734665 x^25 + 51575533686 x^24 + 289157705424 x^23 + 1253334719652 x^22 + 4339842816598 x^21 + 12089938835312 x^20 + 27595185140132 x^19 + 51899069651452 x^18 + 81237872407883 x^17 + 106097483667238 x^16 + 116126611566624 x^15 + 106417824457960 x^14 + 81632991696988 x^13 + 52161861060464 x^12 + 27621327391332 x^11 + 11998025297736 x^10 + 4224689442543 x^9 + 1183463783138 x^8 + 257650398544 x^7 + 42074808244 x^6 + 4911799606 x^5 + 379785344 x^4 + 17289788 x^3 + 373804 x^2 + 2525 x + 2) / ((x - 1)^21 (x + 1)^15), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 02 2013 *)

Crossrefs

Cf. A172123, A172124, A172127, A172129, A176886, A187239 - A187241.

Sequence in context: A013832 A320862 A034989 * A159410 A351781 A016878

Adjacent sequences: A187239 A187240 A187241 * A187243 A187244 A187245

Keyword

nonn,easy,changed

Author

Vaclav Kotesovec, Mar 07 2011

Status

approved