A303542 -id:A303542 - cp's OEIS frontend

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

0, 0, 1, 6, 34, 194, 1275, 10196, 99916, 1164684, 15912733, 250678314, 4507337214, 91329638814, 2069998845799, 52044680125128, 1443501036281272, 43878538143611192, 1455221004684341721, 52393847060853213806, 2040530475078456780538, 85617882485110184661402

Offset: 1

Eric W. Weisstein, Feb 12 2024

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Bishop Graph.
Eric Weisstein's World of Mathematics, Chordless Cycle.

Cf. A370210 (black bishop), A303542 (white bishop), A370228.

\\ see also program in A303542.
CCGenRook(sig)={
 my(p=0,s=0,x='x,y='y);
 forstep(i=#sig, 1, -1, my(w=sig[i]);
   if(i<#sig, p *= y^(w-sig[i+1]));
   s += polcoef(p,1,x);
   p += x*deriv(deriv(p+y^w,y),y)/2 + 2*x*deriv(deriv(p,x),x) + 2*x*deriv(deriv(p,y),x);
   p -= x^i*polcoef(p,i,x);
 );
 s;
}
Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));
a(n) = subst(CCGenRook(Bishop(n,0)) + CCGenRook(Bishop(n,1)), y, 1) \\ Andrew Howroyd, May 27 2025

For n > 1, a(n) = A370210(n) + A303542(n).

a(21) onwards from Andrew Howroyd, May 27 2025

A370210 Number of chordless cycles in the n X n black bishop graph.

Original entry on oeis.org

0, 0, 0, 3, 15, 97, 597, 5098, 47746, 582342, 7691278, 125339157, 2195109753, 45664819407, 1013323126923, 26022340062564, 709267685968788, 21939269071805596, 717007984481424300, 26196923530426606903, 1007535882284116545523, 42808941242555092330701

Offset: 1

Eric W. Weisstein, Feb 12 2024

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Black Bishop Graph.
Eric Weisstein's World of Mathematics, Chordless Cycle.

Cf. A303542 (white bishop graph), A370224 (bishop graph).

\\ CCGenRook, Bishop defined in A370224.
a(n) = subst(CCGenRook(Bishop(n,0)), y, 1) \\ Andrew Howroyd, May 27 2025

For n > 1, a(n) = A370224(n) - A303542(n).

a(21) onwards from Andrew Howroyd, May 27 2025

cp's OEIS Frontend

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

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