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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.

%I A334357 #11 Feb 16 2025 08:34:00
%S A334357 0,1,72,7173,610160,28654530,723903411,11151501102,117740542158,
%T A334357 928786063095,5822688352360,30338870238171,135818642249082,
%U A334357 535712216425568,1898338161488055,6136965479845740,18323823959847156,51039512178104637,133722394132080528
%N 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.
%C A334357 Adjacent vertices may not have the same color.
%C A334357 a(n) is the number of nonequivalent n-colorings of the tesseract graph up to graph isomorphism.
%H A334357 Andrew Howroyd, <a href="/A334357/b334357.txt">Table of n, a(n) for n = 1..1000</a>
%H A334357 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H A334357 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TesseractGraph.html">Tesseract Graph</a>
%H A334357 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexColoring.html">Vertex Coloring</a>
%H A334357 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F A334357 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.
%F A334357 a(n) = Sum_{k=1..16} n^k * A334358(4,16-k) / 384.
%Y A334357 Cf. A128767, A158348, A334356, A334358.
%K A334357 nonn,easy
%O A334357 1,3
%A A334357 _Andrew Howroyd_, Apr 24 2020