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

Author

Marko Riedel, Jun 24 2018

Keywords

• tabl
• nonn
• easy

Examples

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

Links

• Marko Riedel et al., coloring cube sides and vertices

Crossrefs

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

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).