A323500 Number of minimum dominating sets in the n X n black bishop graph.

1, 2, 1, 5, 52, 22, 6, 108, 2964, 672, 120, 4680, 245520, 38160, 5040, 342720, 29292480, 3467520, 362880, 38102400, 4819046400, 460857600, 39916800, 5987520000, 1050690009600, 84304281600, 6227020800, 1264085222400, 293878019635200, 20312541849600

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

Eric Weisstein's World of Mathematics, Black Bishop Graph

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Formula

From Andrew Howroyd, Sep 09 2019: (Start)

a(n) = (n/2)! * (n + 1)/2 for n mod 4 = 0;

a(n) = ((n-1)/2)! * (n^3 + 3*n^2 + 2*n - 2)/8 for n mod 4 = 1, n > 1;

a(n) = (n/2-1)! * (n^2 + n + 2)/4 for n mod 4 = 2;

a(n) = ((n-1)/2)! for n mod 4 = 3.

(End)

Prog

(PARI) \\ See A286886 for DomSetCount, Bishop.
a(n)={Vec(DomSetCount(Bishop(n, 0), x + O(x^((n+3)\2))))[1]} \\ Andrew Howroyd, Sep 08 2019
(PARI) a(n)=if(n==1, 1, (n\4*2)!*if(n%4<2, if(n%2==0, (n+1)/2, (n^3 + 3*n^2 + 2*n - 2)/8), if(n%2==0, (n^2+n+2)/4, (n-1)/2))); \\ Andrew Howroyd, Sep 09 2019

Crossrefs

Cf. A182333 (bishop graph), A323501 (white bishop graph).

Cf. A286886, A289164, A303141.

Sequence in context: A187618 A320101 A343018 * A277471 A110863 A215219

Adjacent sequences: A323497 A323498 A323499 * A323501 A323502 A323503

Keyword

nonn

Author

Eric W. Weisstein, Jan 16 2019

Extensions

Terms a(11) and beyond from Andrew Howroyd, Sep 08 2019

Status

approved