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A338953
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Number of unoriented colorings of the 96 edges (or triangular faces) of the 4-D 24-cell using subsets of a set of n colors.
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9
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1, 68774446639102959610154176, 5523164445430505961199114292414803649442426, 5448873034189827051954635848284422749083650351583379456, 10956401461402941741829572441752281718329313621842215239237500000
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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 one when enumerating unoriented arrangements. The Schläfli symbol of the 24-cell is {3,4,3}. It has 24 octahedral facets. It is self-dual.
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LINKS
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FORMULA
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a(n) = (96*n^8 + 144*n^12 + 144*n^16 + 128*n^18 + 192*n^20 + 228*n^24 +
48*n^32 + 32*n^36 + 43*n^48 + 72*n^50 + 12*n^52 + 12*n^60 + n^96) / 1152.
a(n) = Sum_{j=1..Min(n,96)} A338957(n) * binomial(n,j).
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MATHEMATICA
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Table[(96n^8+144n^12+144n^16+128n^18+192n^20+228n^24+48n^32+32n^36+43n^48+72n^50+12n^52+12n^60+n^96)/1152, {n, 15}]
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CROSSREFS
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Cf. A338952 (oriented), A338954 (chiral), A338955 (achiral), A338957 (exactly n colors), A338949 (vertices, facets), A063843 (5-cell), A331359 (8-cell edges, 16-cell faces), A331355 (16-cell edges, 8-cell faces), A338965 (120-cell, 600-cell).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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