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%I #24 Sep 12 2015 11:00:21
%S 0,0,0,0,100,576,2156,7168,17496,41600,82280,161280,280540,486080,
%T 774900,1232896,1844976,2757888,3933456,5606400,7699860,10570560,
%U 14081980,18754560,24365000,31647616,40258296,51204608,63979916
%N Number of ways to place 3 nonattacking queens on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A172518/b172518.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).
%F 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
%F 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
%t 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 *)
%t 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 *)
%Y Cf. A047659, A007705, A172517.
%K nonn,nice,easy
%O 1,5
%A _Vaclav Kotesovec_, Feb 05 2010
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