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

Author

Eric W. Weisstein, Apr 19 2018

Keywords

• nonn

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

Crossrefs

Cf. A292073, A303212, A347922.

Programs

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

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

Extensions

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