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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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=2..22. 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 Adjacent sequences: A303539 A303540 A303541 * A303543 A303544 A303545 KEYWORD nonn AUTHOR Eric W. Weisstein, Apr 25 2018 EXTENSIONS a(8)-a(22) from Andrew Howroyd, Apr 29 2018 STATUS approved

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Last modified August 7 02:33 EDT 2024. Contains 375003 sequences. (Running on oeis4.)