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A334357
Number of nonequivalent proper colorings of the vertices of a 4D hypercube using at most n colors up to rotations and reflections of the cube.
3
0, 1, 72, 7173, 610160, 28654530, 723903411, 11151501102, 117740542158, 928786063095, 5822688352360, 30338870238171, 135818642249082, 535712216425568, 1898338161488055, 6136965479845740, 18323823959847156, 51039512178104637, 133722394132080528
OFFSET
1,3
COMMENTS
Adjacent vertices may not have the same color.
a(n) is the number of nonequivalent n-colorings of the tesseract graph up to graph isomorphism.
LINKS
Eric Weisstein's World of Mathematics, Hypercube Graph
Eric Weisstein's World of Mathematics, Tesseract Graph
Eric Weisstein's World of Mathematics, Vertex Coloring
Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
FORMULA
a(n) = n*(n - 1)*(n^14 - 31*n^13 + 465*n^12 - 4471*n^11 + 30805*n^10 - 161035*n^9 + 659293*n^8 - 2149343*n^7 + 5610000*n^6 - 11666144*n^5 + 19009100*n^4 - 23485632*n^3 + 20729104*n^2 - 11646800*n + 3125472)/384.
a(n) = Sum_{k=1..16} n^k * A334358(4,16-k) / 384.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, Apr 24 2020
STATUS
approved