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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
OFFSET
1,5
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
KEYWORD
nonn,nice,easy
AUTHOR
Vaclav Kotesovec, Feb 05 2010
STATUS
approved