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A334357
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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.
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2
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0, 1, 72, 7173, 610160, 28654530, 723903411, 11151501102, 117740542158, 928786063095, 5822688352360, 30338870238171, 135818642249082, 535712216425568, 1898338161488055, 6136965479845740, 18323823959847156, 51039512178104637, 133722394132080528
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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FORMULA
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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