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A292073
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Number of dominating sets in the n X n rook complement graph.
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4
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1, 9, 421, 64727, 33548731, 68719441881, 562949953225997, 18446744073708516927, 2417851639229258344138819, 1267650600228229401496677076985, 2658455991569831745807614120434020301, 22300745198530623141535718272648360902500919
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OFFSET
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1,2
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COMMENTS
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Non-dominating sets are just those that are contained in the union of a single row and column minus the intersecting vertex. - Andrew Howroyd, Sep 13 2017
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LINKS
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FORMULA
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a(n) = 2^(n^2) - 2*n*(2^n - 2) + n^2 - n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2 - 2*binomial(n,2)^2 - 1 for n > 1. - Andrew Howroyd, Sep 13 2017
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MATHEMATICA
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Table[If[n == 1, 1, 2^n^2 + (2^n (n - 2) - 4^(n - 1) n + (n - 1)^2 n/2 + 4) n - 1], {n, 20}]
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PROG
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(PARI) a(n) = if(n == 1, 1, 2^(n^2) - 2*n*(2^n - 2) + n^2 - n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2 - 2*binomial(n, 2)^2 - 1); \\ Andrew Howroyd, Sep 13 2017
(Magma) [1] cat [2^(n^2)-2*n*(2^n-2)+n^2-n^2*(2^(n-1)-1)^2+ n^2*(n-1)^2-2*Binomial(n, 2)^2-1: n in [2..15]]; // Vincenzo Librandi, Mar 17 2018
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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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STATUS
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approved
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