A303542 - OEIS

%I #20 Feb 12 2024 08:37:10

%S 0,1,3,19,97,678,5098,52170,582342,8221455,125339157,2312227461,

%T 45664819407,1056675718876,26022340062564,734233350312484,

%U 21939269071805596,738213020202917421,26196923530426606903,1032994592794340235015,42808941242555092330701

%N Number of chordless cycles in the n X n white bishop graph.

%C The chordless cycles in a bishop graph are those cycles which have at most one edge on any diagonal or antidiagonal. - _Andrew Howroyd_, Apr 29 2018

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>

%F For n > 1, a(n) = A370224(n) - A370210(n).

%o (PARI)

%o SafeMat(m)={my(d=matsize(m));((j,k)->if(j>0&&j<=d[1]&&k>0&&k<=d[2], m[j,k]))}

%o CC(sig,x)={my(v=SafeMat([;]), total=0);

%o forstep(i=#sig, 2, -1, my(t=sig[i]);

%o    v=SafeMat(matrix(t, t\2, j, k, v(j,k) + x*(if(j==2&&k==1, binomial(t,2)) + v(j-2,k-1)*binomial(t-j+2,2) + v(j-1,k)*2*k*(t-j+1) + v(j,k+1)*2*k*(k+1))));

%o    total+=sum(j=1,t,v(j,1)) );

%o total}

%o Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));

%o a(n) = CC(Bishop(n,1),1) \\ _Andrew Howroyd_, Apr 29 2018

%Y Cf. A070968.

%Y Cf. A370210 (black bishop), A370224 (bishop).

%K nonn

%O 2,3

%A _Eric W. Weisstein_, Apr 25 2018

%E a(8)-a(22) from _Andrew Howroyd_, Apr 29 2018