A316093 Non-isomorphic colorings of the cube under rotations, using at most N colors on the faces and M colors on the vertices. Square array H(N,M) with N,M > 0 read by antidiagonals.

1, 10, 23, 57, 776, 333, 240, 8121, 17946, 2916, 800, 44608, 200961, 176160, 16725, 2226, 168675, 1124208, 1995852, 1045050, 70911, 5390, 501528, 4281300, 11198720, 11877825, 4485960, 241913, 11712, 1261701, 12773538, 42697300, 66700400, 51044337, 15385706, 701968, 23355, 2807296, 32195646, 127461216, 254387500, 286724160, 175153881, 44761216, 1798281, 43450, 5685903, 71718336, 321364540, 759518850, 1093653675, 983988208, 509689776, 114826410, 4173775

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Marko Riedel et al., coloring cube sides and vertices

Formula

H(N,M) = (1/24) (N^6 M^8 + 6 N^3 M^2 + 3 N^4 M^4 + 8 N^2 M^4 + 6 N^3 M^4).

Cycle index is (1/24)*(a1^6 b1^8 + 6 a1^2 a4 b4^2 + 3 a1^2 a2^2 b2^4 + 8 a3^2 b1^2 b3^2 + 6 a2^3 b2^4).

Example

Square array begins:
     1,     10,      57,      240,      800, ...
    23,    776,    8121,    44608,   168675, ...
   333,  17946,  200961,  1124208,  4281300, ...
  2916, 176160, 1995852, 11198720, 42697300, ...

Crossrefs

H(N,1) (first row) is A047780. H(1,M) (first column) is A000543.

Sequence in context: A135277 A156202 A266080 * A262485 A219940 A164578

Adjacent sequences: A316090 A316091 A316092 * A316094 A316095 A316096

Keyword

tabl,nonn,easy

Author

Marko Riedel, Jun 24 2018

Status

approved