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 A338958 Number of chiral pairs of colorings of the 96 edges (or triangular faces) of the 4-D 24-cell using exactly n colors. 5
 68774446614978208476646592, 5523164445430504871588714239322107782006441, 5448873034167734394145221152621861950913444709790439644, 10956401434158576570935650756489255491646473924447332613392130825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Each member of a chiral pair is a reflection but not a rotation of the other. 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. LINKS Robert A. Russell, Table of n, a(n) for n = 2..96 FORMULA A338954(n) = Sum_{j=2..Min(n,96)} a(n) * binomial(n,j). a(n) = A338956(n) - A338957(n) = (A338956(n) - A338959(n)) / 2 = A338957(n) - A338959(n). MATHEMATICA bp[j_] := Sum[k! StirlingS2[j, k] x^k, {k, 0, j}] (*binomial series*) Drop[CoefficientList[bp/12+bp/8-bp/24-bp/18-bp/6-5bp/96+bp/24+bp/36-5bp/1152+bp/16-bp/96-bp/96+bp/1152, x], 2] CROSSREFS Cf. A338956 (oriented), A338957 (unoriented), A338959 (achiral), A338954 (up to n colors), A338950 (vertices, facets), A331352 (5-cell), A331360 (8-cell edges, 16-cell faces), A331356 (16-cell edges, 8-cell faces), A338982 (120-cell, 600-cell). Sequence in context: A246288 A246255 A338609 * A338954 A338957 A338953 Adjacent sequences:  A338955 A338956 A338957 * A338959 A338960 A338961 KEYWORD fini,nonn,full AUTHOR Robert A. Russell, Nov 17 2020 STATUS approved

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Last modified July 28 17:47 EDT 2021. Contains 346335 sequences. (Running on oeis4.)