A177759 Number of ways to place 6 nonattacking bishops on an n X n toroidal board.

0, 0, 0, 0, 0, 2304, 35280, 811008, 5080320, 38784000, 153679680, 699678720, 2120152320, 7113012480, 18036018000, 49416536064, 110279070720, 261526745088, 530024705280, 1128038400000

Offset

1,6

Links

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

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

Index entries for linear recurrences with constant coefficients, signature (2, 10, -22, -44, 110, 110, -330, -165, 660, 132, -924, 0, 924, -132, -660, 165, 330, -110, -110, 44, 22, -10, -2, 1).

Formula

Explicit formula: 1/1440*(n-4)^2*(n-2)^2*n^2*(2*n^6 -36*n^5 +269*n^4 -1128*n^3 +3143*n^2-6330*n +7425 +(15*n^4 -240*n^3 +1545*n^2 -4950*n +6975)*(-1)^n).

G.f.: -48*x^6*(15*x^17 +2386*x^16 +6778*x^15 +133898*x^14 +235216*x^13 +1520054*x^12 +1844806*x^11 +5402462*x^10+4378450*x^9 +6819710*x^8 +3509350*x^7 +3079094*x^6+926032*x^5 +445642*x^4 +65754*x^3 +14946*x^2 +639*x+48)/((x-1)^13*(x+1)^11).

Mathematica

CoefficientList[Series[- 48 x^5 * (15 x^17 + 2386 x^16 + 6778 x^15 + 133898 x^14 + 235216 x^13 + 1520054 x^12 + 1844806 x^11 + 5402462 x^10 + 4378450 x^9 + 6819710 x^8 + 3509350 x^7 + 3079094 x^6 + 926032 x^5 + 445642 x^4 + 65754 x^3 + 14946 x^2 + 639 x + 48) / ((x - 1)^13  (x+1)^11), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)
LinearRecurrence[{2, 10, -22, -44, 110, 110, -330, -165, 660, 132, -924, 0, 924, -132, -660, 165, 330, -110, -110, 44, 22, -10, -2, 1}, {0, 0, 0, 0, 0, 2304, 35280, 811008, 5080320, 38784000, 153679680, 699678720, 2120152320, 7113012480, 18036018000, 49416536064, 110279070720, 261526745088, 530024705280, 1128038400000, 2120098821120, 4148067559680, 7337013702480, 13421018603520}, 30] (* Harvey P. Dale, Aug 20 2024 *)

Crossrefs

Cf. A176886, A177755, A177756, A177757, A177758.

Sequence in context: A195652 A256729 A204102 * A218431 A187292 A235423

Adjacent sequences: A177756 A177757 A177758 * A177760 A177761 A177762

Keyword

nonn,easy

Author

Vaclav Kotesovec, May 13 2010

Status

approved