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

Author

Andrew Howroyd, Apr 24 2020

Keywords

• nonn
• easy

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

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Cubical Graph
• Eric Weisstein's World of Mathematics, Vertex Coloring
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A128766, A140986, A334357, A334358.

Programs

PARI

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

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.