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Number of total dominating sets in the n-hypercube graph.
1

%I #40 Apr 18 2018 11:26:55

%S 1,9,121,33489,2089129849,8522269792371679969

%N Number of total dominating sets in the n-hypercube graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>

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

%F a(n) = A284704(n-1)^2. - _Andrew Howroyd_, Apr 16 2018

%t Table[Count[Subsets[Range[2^n]], _?(CountDistinct[Flatten[# /. Table[k -> AdjacencyList[HypercubeGraph[n], k], {k, 2^n}]]] == 2^n &)], {n, 1, 3}] (* _Eric W. Weisstein_, Apr 17 2018 *)

%Y Cf. A284704, A290406.

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_, Apr 16 2018

%E a(5)-a(6) from _Andrew Howroyd_, Apr 16 2018