A334356 Number of nonequivalent proper colorings of the vertices of a cube using at most n colors up to rotations and reflections of the cube.

0, 1, 15, 154, 1115, 5955, 24836, 85260, 251154, 655005, 1548085, 3374646, 6876805, 13237679, 24271170, 42667640, 72305556, 118640025, 189179979, 294066610, 446766495, 664893691, 971175920, 1394580804, 1971618950, 2747841525, 3779550801, 5135742990, 6900303529

Offset

1,3

Comments

Adjacent vertices may not have the same color.

a(n) is the number of nonequivalent n-colorings of the cubical graph up to graph isomorphism.

Links

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Cubical Graph

Eric Weisstein's World of Mathematics, Vertex Coloring

Formula

a(n) = n*(n - 1)*(n^6 - 11*n^5 + 61*n^4 - 195*n^3 + 384*n^2 - 428*n + 216)/48.

a(n) = Sum_{k=1..8} n^k * A334358(3,8-k) / 48.

Prog

(PARI) a(n) = {n*(n - 1)*(n^6 - 11*n^5 + 61*n^4 - 195*n^3 + 384*n^2 - 428*n + 216)/48}

Crossrefs

Cf. A128766, A140986, A334357, A334358.

Sequence in context: A125403 A010035 A370765 * A017389 A278803 A157380

Adjacent sequences: A334353 A334354 A334355 * A334357 A334358 A334359

Keyword

nonn

Author

Andrew Howroyd, Apr 24 2020

Status

approved