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Number of chiral pairs of colorings of the 120 dodecahedral facets of the 4-D 120-cell (or 120 vertices of the 4-D 600-cell) using exactly n colors.
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6
0, 1, 314843647550280564734, 5068890957389326592282175518285751, 11893730796581701705423717900461048616681772, 220581437248293418784474364671733389683204494492535
Number of achiral colorings of the 120 dodecahedral facets of the 4-D 120-cell (or 120 vertices of the 4-D 600-cell) using subsets of a set of n colors.
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13
1, 314843647550280564736, 5068890957390271123224826359979956, 11893730816857265534982913331475052373213184, 220581496716947452381892465686737251285705566406250
Number of achiral colorings of the 24 octahedral facets (or 24 vertices) of the 4-D 24-cell using subsets of a set of n colors.
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11
1, 6504, 8416440, 1455789440, 80139247500, 2125945744776, 34026498820524, 376045864704000, 3131319814422255, 20854395850585000, 115919421344402676, 554976171149122944, 2343894146343268610, 8896568181794053320
Number of unoriented colorings of the 8 cubic facets of a tesseract or of the 8 vertices of a hyperoctahedron.
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8
1, 15, 126, 715, 3060, 10626, 31465, 82251, 194580, 424270, 864501, 1663740, 3049501, 5359095, 9078630, 14891626, 23738715, 36890001, 56031760, 83369265, 121747626, 174792640, 247073751, 344291325, 473490550, 643304376
Number of oriented colorings of the 8 cubic facets of a tesseract or of the 8 vertices of a hyperoctahedron.
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8
1, 15, 126, 730, 3270, 11991, 37450, 102726, 253485, 573265, 1205556, 2384460, 4475926, 8031765, 13858860, 23106196, 37372545, 58837851, 90421570, 135971430, 200486286, 290376955, 413769126, 580852650, 804281725
Number of achiral colorings of the 16 tetrahedral facets of a hyperoctahedron or of the 16 vertices of a tesseract.
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8
1, 308, 34128, 1056576, 15303750, 136236276, 865711763, 4296782848, 17656466751, 62510672500, 196174554026, 557301826368, 1456216515468, 3543525156276, 8109415963125, 17592637669376, 36414622551373
Number of ways to choose 4 points in an n X n X n triangular grid.
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11
15, 210, 1365, 5985, 20475, 58905, 148995, 341055, 720720, 1426425, 2672670, 4780230, 8214570, 13633830, 21947850, 34389810, 52602165, 78738660, 115584315, 166695375, 236561325, 330791175, 456326325, 621682425, 837222750, 1115465715, 1471429260, 1923014940
Partial sum of centered tetrahedral numbers A005894.
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12
1, 6, 21, 56, 125, 246, 441, 736, 1161, 1750, 2541, 3576, 4901, 6566, 8625, 11136, 14161, 17766, 22021, 27000, 32781, 39446, 47081, 55776, 65625, 76726, 89181, 103096, 118581, 135750, 154721, 175616, 198561, 223686, 251125, 281016, 313501, 348726, 386841
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