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Number of different ways to color the vertices of an n-dimensional hypercube using at most 2 colors.
1

%I #23 May 23 2022 03:52:36

%S 4,6,23,496,2275974,800648638402240,

%T 1054942853799126580390222487977120,

%U 22436153203535039105819651040959324360753617244078062654624560815030272

%N Number of different ways to color the vertices of an n-dimensional hypercube using at most 2 colors.

%C Two colorings are regarded as the same if they are conjugated by a permutation of the vertices caused by a rotation of the hypercube.

%C Regarding mirrored coloring also as the same, the number of ways appears to be given by A000616. - _Azuma Seiichi_, Feb 14 2014

%H Azuma Seiichi, <a href="http://searial.web.fc2.com/hypercube/index.html">Number of different ways to color vertices of a n-dimensional hypercube using at most K colors</a>

%e For n=2, there are 6 patterns to color the vertices of the square:

%e ..1..1....1..1....1..1....1..0....1..0....0..0

%e ..1..1....1..0....0..0....0..1....0..0....0..0

%e For example, the next pattern is regarded as the same with the 3rd one above:

%e ..1..0

%e ..1..0

%Y Cf. A000543.

%Y Column 2 of A325012.

%K nonn

%O 1,1

%A _Azuma Seiichi_, Feb 12 2014