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A303209 Number of total dominating sets in the n X n rook complement graph. 1
0, 1, 334, 63935, 33543096, 68719407273, 562949953031502, 18446744073707484655, 2417851639229258338871776, 1267650600228229401496650964865, 2658455991569831745807614120307390270, 22300745198530623141535718272648360299110799 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Non-dominating sets are just those that are contained in the union of a single row and column. - Andrew Howroyd, Apr 20 2018

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50

Eric Weisstein's World of Mathematics, Rook Complement Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

FORMULA

a(n) = 2^(n^2) - 2*n*(2^n - 1) - 2*n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2/2 + n^2 - 1. - Andrew Howroyd, Apr 20 2018

PROG

(PARI) a(n) = {2^(n^2) - 2*n*(2^n - 1) - 2*n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2/2 + n^2 - 1} \\ Andrew Howroyd, Apr 20 2018

CROSSREFS

Cf. A292073, A303212.

Sequence in context: A184463 A303210 A278098 * A216138 A252995 A119760

Adjacent sequences:  A303206 A303207 A303208 * A303210 A303211 A303212

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Apr 19 2018

EXTENSIONS

Terms a(6) and beyond from Andrew Howroyd, Apr 20 2018

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)