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A338956
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Number of oriented colorings of the 96 edges (or triangular faces) of the 4-D 24-cell using exactly n colors.
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5
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1, 137548893254081168086800766, 11046328890861010626464488614428032600986342, 10897746068335468788318134977474134922662053604436974448, 21912802868317153141871319582922663027477920477404414535105616050
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OFFSET
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1,2
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COMMENTS
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Each chiral pair is counted as two when enumerating oriented arrangements. The Schläfli symbol of the 24-cell is {3,4,3}. It has 24 octahedral facets. It is self-dual. For n>96, a(n) = 0.
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LINKS
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FORMULA
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A338952(n) = Sum_{j=1..Min(n,96)} a(n) * binomial(n,j).
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MATHEMATICA
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bp[j_] := Sum[k! StirlingS2[j, k] x^k, {k, 0, j}] (* binomial series *)
Drop[CoefficientList[bp[8]/6+bp[12]/4+bp[16]/12+bp[18]/18+7bp[24]/48+bp[32]/12+bp[36]/18+19bp[48]/576+bp[50]/8+bp[96]/576, x], 1]
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CROSSREFS
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Cf. A338957 (unoriented), A338958 (chiral), A338959 (achiral), A338952 (up to n colors), A338948 (vertices, facets), A331350 (5-cell), A331358 (8-cell edges, 16-cell faces), A331354 (16-cell edges, 8-cell faces), A338980 (120-cell, 600-cell).
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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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