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 A292073 Number of dominating sets in the n X n rook complement graph. 4
 1, 9, 421, 64727, 33548731, 68719441881, 562949953225997, 18446744073708516927, 2417851639229258344138819, 1267650600228229401496677076985, 2658455991569831745807614120434020301, 22300745198530623141535718272648360902500919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..50 Eric Weisstein's World of Mathematics, Dominating Set Eric Weisstein's World of Mathematics, Rook Complement Graph FORMULA 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 MATHEMATICA 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}] PROG (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 CROSSREFS Cf. A291623, A292074. Sequence in context: A091061 A024123 A218140 * A232249 A229843 A081481 Adjacent sequences: A292070 A292071 A292072 * A292074 A292075 A292076 KEYWORD nonn AUTHOR Eric W. Weisstein, Sep 12 2017 EXTENSIONS a(6)-a(12) from Andrew Howroyd, Sep 13 2017 STATUS approved

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Last modified August 15 04:20 EDT 2024. Contains 375172 sequences. (Running on oeis4.)