cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A334247 Number of acyclic orientations of the edges of an n-dimensional cube.

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%I A334247 #37 Feb 16 2025 08:34:00
%S A334247 1,2,14,1862,193270310,47171704165698393638
%N A334247 Number of acyclic orientations of the edges of an n-dimensional cube.
%C A334247 a(n) is the absolute value of the chromatic polynomial of the n-hypercube graph evaluated at -1.
%H A334247 David Eppstein, <a href="https://commons.wikimedia.org/wiki/File:Acyclic_orientations_of_C4.svg">14 acyclic orientations of a square</a>
%H A334247 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%F A334247 a(n) = Sum_{k=1..2^n} (-1)^(2^n-k) * k! * A334159(n, k). - _Andrew Howroyd_, Apr 21 2020
%F A334247 a(n) = |Sum_{k=0..2^n} (-1)^k * A334278(n, k)|. - _Peter Kagey_, Oct 13 2020
%e A334247 For n=2, there are 14 ways to orient the edges of a square without cycles (see links).
%p A334247 with(GraphTheory): with(SpecialGraphs):
%p A334247 a:= n-> abs(ChromaticPolynomial(HypercubeGraph(n), -1)):
%p A334247 seq(a(n), n=0..4);  # _Alois P. Heinz_, Jan 14 2025
%Y A334247 Cf. A334248 is the number of acyclic orientations with rotations and reflections of the same orientation excluded.
%Y A334247 Cf. A140986, A158348, A296914, A334159, A334278.
%Y A334247 Cf. A033815 (cross-polytope), A058809 (wheel), A338152 (demihypercube), A338153 (prism), A338154 (antiprism).
%K A334247 nonn,more
%O A334247 0,2
%A A334247 _Matthew Scroggs_, Apr 20 2020
%E A334247 a(5) from _Andrew Howroyd_, Apr 23 2020