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A177757
Number of ways to place 4 nonattacking bishops on an n X n toroidal board.
5
0, 0, 0, 64, 600, 6912, 29400, 132864, 381024, 1139200, 2613600, 6177600, 12269400, 24912384, 44717400, 81636352, 135945600, 229423104, 360561024, 572788800, 859685400, 1301766400, 1881864600, 2740725504, 3840540000
OFFSET
1,4
LINKS
V. Kotesovec, Non-attacking chess pieces, 6ed, 2013
Index entries for linear recurrences with constant coefficients, signature (2,6,-14,-14,42,14,-70,0,70,-14,-42,14,14,-6,-2,1).
FORMULA
a(n) = 1/48*(n-2)^2*n^2*(2n^4 -16n^3 +50n^2 -84n +81 +(6n^2 -36n +63)*(-1)^n).
G.f.: -8x^4*(3x^11 +122x^10 +401x^9 +2508x^8 +3316x^7 +7780x^6 +5172x^5 +5236x^4 +1609x^3 +666x^2 +59x+8)/((x-1)^9*(x+1)^7).
MATHEMATICA
CoefficientList[Series[- 8 x^3 (3 x^11 + 122 x^10 + 401 x^9 + 2508 x^8 + 3316 x^7 + 7780 x^6 + 5172 x^5 + 5236 x^4 + 1609 x^3 + 666 x^2 + 59 x + 8)/((x - 1)^9 (x + 1)^7), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)
LinearRecurrence[{2, 6, -14, -14, 42, 14, -70, 0, 70, -14, -42, 14, 14, -6, -2, 1}, {0, 0, 0, 64, 600, 6912, 29400, 132864, 381024, 1139200, 2613600, 6177600, 12269400, 24912384, 44717400, 81636352}, 50] (* Harvey P. Dale, Nov 05 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, May 13 2010
STATUS
approved