A338957
Number of unoriented colorings of the 96 edges (or triangular faces) of the 4-D 24-cell using exactly n colors.
Original entry on oeis.org
1, 68774446639102959610154174, 5523164445430505754875774375105924818979901, 5448873034167734394172913824852272971748608894646534804, 10956401434158576570935668826433407535831446552957081921713485225
Offset: 1
Cf.
A338956 (oriented),
A338958 (chiral),
A338959 (achiral),
A338953 (up to n colors),
A338949 (vertices, facets),
A063843 (5-cell),
A331359 (8-cell edges, 16-cell faces),
A331355 (16-cell edges, 8-cell faces),
A338981 (120-cell, 600-cell).
-
bp[j_] := Sum[k! StirlingS2[j, k] x^k, {k, 0, j}] (* binomial series *)
Drop[CoefficientList[bp[8]/12+bp[12]/8+bp[16]/8+bp[18]/9+bp[20]/6+19bp[24]/96+bp[32]/24+bp[36]/36+43bp[48]/1152+bp[50]/16+bp[52]/96+bp[60]/96+bp[96]/1152,x],1]
A333418
Irregular triangle: T(n,k) gives the number of ways to 2-color k edges of the n-cube up to rotation and reflection, with 0 <= k <= A001787(n).
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 9, 18, 24, 30, 24, 18, 9, 4, 1, 1, 1, 1, 6, 24, 140, 604, 2596, 9143
Offset: 1
Table begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 ...
---+-------------------------------------------------------
1| 1, 1;
2| 1, 1, 2, 1, 1;
3| 1, 1, 4, 9, 18, 24, 30, 24, 18, 9, 4, 1, 1;
4| 1, 1, 6, 24, 140, 604, 2596, 9143, ...
5| 1, 1, 8, 50, 608, ...
6| 1, 1, 10, 89, ...
A333444
Number of 2-colorings of edges of the n-cube up to isometry.
Original entry on oeis.org
2, 6, 144, 11251322, 314824456456819827136, 136221825854745676520058554256163406987047485113810944
Offset: 1
Comments