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Number of stable partitions of the n-hypercube graph.
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%I #6 Feb 16 2025 08:34:00

%S 1,1,4,354,179185930,258823757396708888836788

%N Number of stable partitions of the n-hypercube graph.

%C A stable partition is a partition of the vertices into sets so that no two vertices in a set are adjacent in the graph.

%C Equivalently, a(n) is the number of vertex colorings of the n-hypercube graph with any number of unlabeled colors. The vertices are not interchangeable.

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

%e The a(2) = 4 stable partitions of the 2-dimensional hypercube are:

%e 1---2 1---2 1---2 1---2

%e | | | | | | | |

%e 2---1 2---3 3---1 3---4

%Y Row sums of A334159.

%K nonn,changed

%O 0,3

%A _Andrew Howroyd_, Apr 25 2020