A334357 Number of nonequivalent proper colorings of the vertices of a 4D hypercube using at most n colors up to rotations and reflections of the cube.

0, 1, 72, 7173, 610160, 28654530, 723903411, 11151501102, 117740542158, 928786063095, 5822688352360, 30338870238171, 135818642249082, 535712216425568, 1898338161488055, 6136965479845740, 18323823959847156, 51039512178104637, 133722394132080528

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 tesseract graph up to graph isomorphism.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Hypercube Graph
• Eric Weisstein's World of Mathematics, Tesseract Graph
• Eric Weisstein's World of Mathematics, Vertex Coloring
• Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Crossrefs

Cf. A128767, A158348, A334356, A334358.

Formula

a(n) = n*(n - 1)*(n^14 - 31*n^13 + 465*n^12 - 4471*n^11 + 30805*n^10 - 161035*n^9 + 659293*n^8 - 2149343*n^7 + 5610000*n^6 - 11666144*n^5 + 19009100*n^4 - 23485632*n^3 + 20729104*n^2 - 11646800*n + 3125472)/384.

a(n) = Sum_{k=1..16} n^k * A334358(4,16-k) / 384.