cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A338958 Number of chiral pairs of colorings of the 96 edges (or triangular faces) of the 4-D 24-cell using exactly n colors.

This page as a plain text file.
%I A338958 #14 Dec 20 2020 02:21:50
%S A338958 68774446614978208476646592,
%T A338958 5523164445430504871588714239322107782006441,
%U A338958 5448873034167734394145221152621861950913444709790439644,10956401434158576570935650756489255491646473924447332613392130825
%N A338958 Number of chiral pairs of colorings of the 96 edges (or triangular faces) of the 4-D 24-cell using exactly n colors.
%C A338958 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.
%H A338958 Robert A. Russell, <a href="/A338958/b338958.txt">Table of n, a(n) for n = 2..96</a>
%F A338958 A338954(n) = Sum_{j=2..Min(n,96)} a(n) * binomial(n,j).
%F A338958 a(n) = A338956(n) - A338957(n) = (A338956(n) - A338959(n)) / 2 = A338957(n) - A338959(n).
%t A338958 bp[j_] := Sum[k! StirlingS2[j, k] x^k, {k, 0, j}] (*binomial series*)
%t A338958 Drop[CoefficientList[bp[8]/12+bp[12]/8-bp[16]/24-bp[18]/18-bp[20]/6-5bp[24]/96+bp[32]/24+bp[36]/36-5bp[48]/1152+bp[50]/16-bp[52]/96-bp[60]/96+bp[96]/1152,x],2]
%Y A338958 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).
%K A338958 fini,nonn,full
%O A338958 2,1
%A A338958 _Robert A. Russell_, Nov 17 2020