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%I #18 Sep 12 2015 11:00:23
%S 0,4,18,80,200,468,882,1600,2592,4100,6050,8784,12168,16660,22050,
%T 28928,36992,46980,58482,72400,88200,106964,128018,152640,180000
%N Number of ways to place 2 nonattacking bishops on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A177755/b177755.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013
%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 Explicit formula: 1/4*n^2*(2*n^2-4*n+3+(-1)^n).
%F G.f.: -2*x^2*(x^5+8*x^4+14*x^3+18*x^2+5*x+2)/((x-1)^5*(x+1)^3).
%F a(1)=0, a(2)=4, a(3)=18, a(4)=80, a(5)=200, a(6)=468, a(7)=882, a(8)=1600, 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). - _Harvey P. Dale_, Mar 06 2013
%t Table[(n^2 (2n^2-4n+3+(-1)^n))/4,{n,30}] (* or *) LinearRecurrence[ {2,2,-6,0,6,-2,-2,1},{0,4,18,80,200,468,882,1600},30] (* _Harvey P. Dale_, Mar 06 2013 *)
%t CoefficientList[Series[- 2 x (x^5 + 8 x^4 + 14 x^3 + 18 x^2 + 5 x + 2) / ((x - 1)^5 (x + 1)^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, May 31 2013 *)
%Y Cf. A172123.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, May 13 2010
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