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A303542
Number of chordless cycles in the n X n white bishop graph.
2
0, 1, 3, 19, 97, 678, 5098, 52170, 582342, 8221455, 125339157, 2312227461, 45664819407, 1056675718876, 26022340062564, 734233350312484, 21939269071805596, 738213020202917421, 26196923530426606903, 1032994592794340235015, 42808941242555092330701
OFFSET
2,3
COMMENTS
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
LINKS
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, White Bishop Graph
FORMULA
For n > 1, a(n) = A370224(n) - A370210(n).
PROG
(PARI)
SafeMat(m)={my(d=matsize(m)); ((j, k)->if(j>0&&j<=d[1]&&k>0&&k<=d[2], m[j, k]))}
CC(sig, x)={my(v=SafeMat([; ]), total=0);
forstep(i=#sig, 2, -1, my(t=sig[i]);
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))));
total+=sum(j=1, t, v(j, 1)) );
total}
Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));
a(n) = CC(Bishop(n, 1), 1) \\ Andrew Howroyd, Apr 29 2018
CROSSREFS
Cf. A070968.
Cf. A370210 (black bishop), A370224 (bishop).
Sequence in context: A074361 A126187 A215420 * A294251 A294392 A358284
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 25 2018
EXTENSIONS
a(8)-a(22) from Andrew Howroyd, Apr 29 2018
STATUS
approved