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%I #31 Sep 08 2022 08:46:19
%S 1,9,421,64727,33548731,68719441881,562949953225997,
%T 18446744073708516927,2417851639229258344138819,
%U 1267650600228229401496677076985,2658455991569831745807614120434020301,22300745198530623141535718272648360902500919
%N Number of dominating sets in the n X n rook complement graph.
%C Non-dominating sets are just those that are contained in the union of a single row and column minus the intersecting vertex. - _Andrew Howroyd_, Sep 13 2017
%H Vincenzo Librandi, <a href="/A292073/b292073.txt">Table of n, a(n) for n = 1..50</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%F a(n) = 2^(n^2) - 2*n*(2^n - 2) + n^2 - n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2 - 2*binomial(n,2)^2 - 1 for n > 1. - _Andrew Howroyd_, Sep 13 2017
%t Table[If[n == 1, 1, 2^n^2 + (2^n (n - 2) - 4^(n - 1) n + (n - 1)^2 n/2 + 4) n - 1], {n, 20}]
%o (PARI) a(n) = if(n == 1, 1, 2^(n^2) - 2*n*(2^n - 2) + n^2 - n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2 - 2*binomial(n,2)^2 - 1); \\ _Andrew Howroyd_, Sep 13 2017
%o (Magma) [1] cat [2^(n^2)-2*n*(2^n-2)+n^2-n^2*(2^(n-1)-1)^2+ n^2*(n-1)^2-2*Binomial(n,2)^2-1: n in [2..15]]; // _Vincenzo Librandi_, Mar 17 2018
%Y Cf. A291623, A292074.
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Sep 12 2017
%E a(6)-a(12) from _Andrew Howroyd_, Sep 13 2017