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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)