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A172518 Number of ways to place 3 nonattacking queens on an n X n toroidal board. 9
0, 0, 0, 0, 100, 576, 2156, 7168, 17496, 41600, 82280, 161280, 280540, 486080, 774900, 1232896, 1844976, 2757888, 3933456, 5606400, 7699860, 10570560, 14081980, 18754560, 24365000, 31647616, 40258296, 51204608, 63979916 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Index entries for linear recurrences with constant coefficients, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).

FORMULA

a(n) = n^2*(n-2)*(n-4)*(n^2-6*n+12)/6 if n is even and a(n) = n^2*(n-1)*(n-3)*(n^2-8*n+18)/6 if n is odd. - Vaclav Kotesovec, Jan 31 2010

G.f.: -4*x^5*(9*x^6+94*x^5+199*x^4+388*x^3+151*x^2+94*x+25) / ((x-1)^7*(x+1)^5). - Colin Barker, Jan 09 2013

MATHEMATICA

CoefficientList[Series[- 4 x^4 (9 x^6 + 94 x^5 + 199 x^4 + 388 x^3 + 151 x^2 + 94 x + 25) / ((x - 1)^7 (x + 1)^5), {x, 0, 50}], x] ( * Vincenzo Librandi, May 29 2013 *)

LinearRecurrence[{2, 4, -10, -5, 20, 0, -20, 5, 10, -4, -2, 1}, {0, 0, 0, 0, 100, 576, 2156, 7168, 17496, 41600, 82280, 161280}, 30] (* Harvey P. Dale, Dec 27 2014 *)

CROSSREFS

Cf. A047659, A007705, A172517.

Sequence in context: A115695 A250700 A250846 * A174073 A231759 A231046

Adjacent sequences:  A172515 A172516 A172517 * A172519 A172520 A172521

KEYWORD

nonn,nice,easy

AUTHOR

Vaclav Kotesovec, Feb 05 2010

STATUS

approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)