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A370224 Number of chordless cycles in the n X n bishop graph.

%I A370224 #17 May 27 2025 14:59:28
%S A370224 0,0,1,6,34,194,1275,10196,99916,1164684,15912733,250678314,
%T A370224 4507337214,91329638814,2069998845799,52044680125128,1443501036281272,
%U A370224 43878538143611192,1455221004684341721,52393847060853213806,2040530475078456780538,85617882485110184661402
%N A370224 Number of chordless cycles in the n X n bishop graph.
%H A370224 Andrew Howroyd, <a href="/A370224/b370224.txt">Table of n, a(n) for n = 1..200</a>
%H A370224 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BishopGraph.html">Bishop Graph</a>.
%H A370224 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>.
%F A370224 For n > 1, a(n) = A370210(n) + A303542(n).
%o A370224 (PARI) \\ see also program in A303542.
%o A370224 CCGenRook(sig)={
%o A370224  my(p=0,s=0,x='x,y='y);
%o A370224  forstep(i=#sig, 1, -1, my(w=sig[i]);
%o A370224    if(i<#sig, p *= y^(w-sig[i+1]));
%o A370224    s += polcoef(p,1,x);
%o A370224    p += x*deriv(deriv(p+y^w,y),y)/2 + 2*x*deriv(deriv(p,x),x) + 2*x*deriv(deriv(p,y),x);
%o A370224    p -= x^i*polcoef(p,i,x);
%o A370224  );
%o A370224  s;
%o A370224 }
%o A370224 Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));
%o A370224 a(n) = subst(CCGenRook(Bishop(n,0)) + CCGenRook(Bishop(n,1)), y, 1) \\ _Andrew Howroyd_, May 27 2025
%Y A370224 Cf. A370210 (black bishop), A303542 (white bishop), A370228.
%K A370224 nonn
%O A370224 1,4
%A A370224 _Eric W. Weisstein_, Feb 12 2024
%E A370224 a(21) onwards from _Andrew Howroyd_, May 27 2025