%I #12 Feb 16 2025 08:33:54

%S 0,1,334,63935,33543096,68719407273,562949953031502,

%T 18446744073707484655,2417851639229258338871776,

%U 1267650600228229401496650964865,2658455991569831745807614120307390270,22300745198530623141535718272648360299110799

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

%C 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

%H Andrew Howroyd, <a href="/A303209/b303209.txt">Table of n, a(n) for n = 1..50</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>

%F 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

%o (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

%Y Cf. A292073, A303212, A347922.

%K nonn,changed

%O 1,3

%A _Eric W. Weisstein_, Apr 19 2018

%E Terms a(6) and beyond from _Andrew Howroyd_, Apr 20 2018