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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A004322 A125403 A010035 * A017389 A278803 A157380

Adjacent sequences:  A334353 A334354 A334355 * A334357 A334358 A334359

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Apr 24 2020

STATUS

approved

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Last modified April 14 01:17 EDT 2021. Contains 342941 sequences. (Running on oeis4.)