A323501 Number of minimum dominating sets in the n X n white bishop graph.

2, 6, 5, 2, 22, 356, 108, 24, 672, 25056, 4680, 720, 38160, 2531520, 342720, 40320, 3467520, 358444800, 38102400, 3628800, 460857600, 68388364800, 5987520000, 479001600, 84304281600, 16979648716800, 1264085222400, 87178291200, 20312541849600

Offset

2,1

Links

Andrew Howroyd, Table of n, a(n) for n = 2..50

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Eric Weisstein's World of Mathematics, White Bishop Graph

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)! for n mod 4 = 1;

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

a(n) = ((n-3)/2)! * (n + 1)*(n^3 + n^2 - 6*n + 6)/16 for n mod 4 = 3.

(End)

Prog

(PARI) \\ See A289170 for DomSetCount, Bishop.
a(n)={Vec(DomSetCount(Bishop(n, 1), x + O(x^((n+3)\2))))[1]} \\ Andrew Howroyd, Sep 08 2019
(PARI) a(n)=(n\4*2)!*if(n%4<2, if(n%2==0, (n + 1)/2, 1), if(n%2==0, (n^2 + n + 2)/4, (n + 1)*(n^3 + n^2 - 6*n + 6)/16)); \\ Andrew Howroyd, Sep 09 2019

Crossrefs

Cf. A182333 (bishop graph), A323500 (black bishop graph).

Cf. A287897, A289170, A303144.

Sequence in context: A304585 A336074 A021381 * A157890 A329932 A359858

Adjacent sequences: A323498 A323499 A323500 * A323502 A323503 A323504

Keyword

nonn

Author

Eric W. Weisstein, Jan 16 2019

Extensions

Offset corrected and terms a(11) and beyond from Andrew Howroyd, Sep 08 2019

Status

approved