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%I #23 May 28 2021 13:20:16
%S 0,0,0,32,100,288,588,1152,1944,3200,4840,7200,10140,14112,18900,
%T 25088,32368,41472,51984,64800,79380,96800,116380,139392,165000,
%U 194688,227448,264992,306124,352800,403620,460800,522720,591872,666400,749088,837828
%N Number of ways to place 2 nonattacking queens on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A172517/b172517.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F a(n) = n^2*(n-2)^2/2 if n is even and a(n) = n^2*(n-1)(n-3)/2 if n is odd.
%F G.f.: -4*x^4*(x^3+6*x^2+9*x+8) / ((x-1)^5*(x+1)^3). - _Colin Barker_, Jan 09 2013
%F a(n) = 2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8). - _Wesley Ivan Hurt_, May 28 2021
%t CoefficientList[Series[- 4 x^3 (x^3 + 6 x^2 + 9 x + 8) / ((x - 1)^5 (x + 1)^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, May 29 2013 *)
%t LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{0,0,0,32,100,288,588,1152},40] (* _Harvey P. Dale_, Sep 22 2015 *)
%Y Cf. A007705, A036464.
%K nonn,nice,easy
%O 1,4
%A _Vaclav Kotesovec_, Feb 05 2010
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