cp's OEIS Frontend

A215943 Number of ways to place k non-attacking bishops on an n x n toroidal chessboard, summed over all k >= 0.

%I A215943 #11 Jun 02 2025 08:06:48
%S A215943 2,9,34,289,1546,19321,130922,2169729,17572114,364466281,3405357682,
%T A215943 85143154849,896324308634,26309790300249,306827170866106,
%U A215943 10366719612433921,132240988644215842,5064730099043043529,69974827707903049154,3000912883089564050721
%N A215943 Number of ways to place k non-attacking bishops on an n x n toroidal chessboard, summed over all k >= 0.
%C A215943 a(n) = A002720(n) if n is odd.
%H A215943 Vaclav Kotesovec, <a href="/A215943/b215943.txt">Table of n, a(n) for n = 1..440</a>
%H A215943 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%F A215943 Recurrence: a(n) = ((12*n^5 - 158*n^4 - (6*(-1)^n-706)*n^3 - (1193-41*(-1)^n)*n^2 - 8*(7*(-1)^n-72)*n - 22*(-1)^n-28)*a(n-2) + (-12*n^6 + 206*n^5 + 2*(7*(-1)^n-691)*n^4 + (4545-137*(-1)^n)*n^3 + (442*(-1)^n-7442)*n^2 + (5194-544*(-1)^n)*n + 198*(-1)^n-698)*(n-2)*a(n-4) + 2*(2*n-1)*(n^2-7*n+10)^2*(n-4)^4*a(n-6))/(2*(n-5)^2*(2*n-5)).
%t A215943 Table[Sum[If[EvenQ[n],2^k*k!*Sum[Binomial[n/2,i]^2*Binomial[n/2,k-i]^2/Binomial[k,i],{i,0,k}],Binomial[n,k]^2*k!],{k,0,n}],{n,1,25}]
%Y A215943 Cf. A002720, A201862, A010790, A177755-A177759, A178140, A189789, A189790, A189791.
%K A215943 nonn
%O A215943 1,1
%A A215943 _Vaclav Kotesovec_, Aug 28 2012