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A334247
Number of acyclic orientations of the edges of an n-dimensional cube.
7
1, 2, 14, 1862, 193270310, 47171704165698393638
OFFSET
0,2
COMMENTS
a(n) is the absolute value of the chromatic polynomial of the n-hypercube graph evaluated at -1.
LINKS
Eric Weisstein's World of Mathematics, Hypercube Graph
FORMULA
a(n) = Sum_{k=1..2^n} (-1)^(2^n-k) * k! * A334159(n, k). - Andrew Howroyd, Apr 21 2020
a(n) = |Sum_{k=0..2^n} (-1)^k * A334278(n, k)|. - Peter Kagey, Oct 13 2020
EXAMPLE
For n=2, there are 14 ways to orient the edges of a square without cycles (see links).
CROSSREFS
Cf. A334248 is the number of acyclic orientations with rotations and reflections of the same orientation excluded.
Cf. A033815 (cross-polytope), A058809 (wheel), A338152 (demihypercube), A338153 (prism), A338154 (antiprism).
Sequence in context: A347908 A227403 A156736 * A277288 A296412 A296410
KEYWORD
nonn,more
AUTHOR
Matthew Scroggs, Apr 20 2020
EXTENSIONS
a(5) from Andrew Howroyd, Apr 23 2020
STATUS
approved