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A323500
Number of minimum dominating sets in the n X n black bishop graph.
3
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
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).
Sequence in context: A187618 A320101 A343018 * A277471 A110863 A215219
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jan 16 2019
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Sep 08 2019
STATUS
approved