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A323501
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Number of minimum dominating sets in the n X n white bishop graph.
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3
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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
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OFFSET
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2,1
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LINKS
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FORMULA
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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)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Offset corrected and terms a(11) and beyond from Andrew Howroyd, Sep 08 2019
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STATUS
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approved
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