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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
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
Sequence in context: A091061 A024123 A218140 * A232249 A229843 A081481
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 March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)