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%I #11 Jan 19 2022 11:14:14
%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="http://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://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
%O 1,3
%A _Eric W. Weisstein_, Apr 19 2018
%E Terms a(6) and beyond from _Andrew Howroyd_, Apr 20 2018
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