A303209 Number of total dominating sets in the n X n rook complement graph.

0, 1, 334, 63935, 33543096, 68719407273, 562949953031502, 18446744073707484655, 2417851639229258338871776, 1267650600228229401496650964865, 2658455991569831745807614120307390270, 22300745198530623141535718272648360299110799

Offset

1,3

Comments

The vertex sets which are not totally dominating 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, A347922.

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