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

1,3

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

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Hypercube Graph

Eric Weisstein's World of Mathematics, Tesseract Graph

Eric Weisstein's World of Mathematics, Vertex Coloring

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.

Crossrefs

Cf. A128767, A158348, A334356, A334358.

Sequence in context: A216705 A223148 A289368 * A119750 A283093 A178635

Adjacent sequences: A334354 A334355 A334356 * A334358 A334359 A334360

Keyword

nonn

Author

Andrew Howroyd, Apr 24 2020

Status

approved