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A338153
a(n) is the number of acyclic orientations of the edges of the n-prism.
4
204, 1862, 14700, 109334, 790524, 5633222, 39828300, 280376054, 1968934044, 13807724582, 96754776300, 677686169174, 4745413960764, 33224340503942, 232596153986700, 1628276158432694, 11398345428510684, 79790067272259302, 558537067986067500, 3909785864202510614
OFFSET
3,1
COMMENTS
Conjectured linear recurrence and g.f. confirmed by Kagey's formula. - Ray Chandler, Mar 10 2024
LINKS
Eric Weisstein's World of Mathematics, Prism Graph
FORMULA
Conjectures from Colin Barker, Oct 13 2020: (Start)
G.f.: 2*x^3*(102 - 497*x + 742*x^2 - 392*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 7*x)).
a(n) = 14*a(n-1) - 63*a(n-2) + 106*a(n-3) - 56*a(n-4) for n>6.
(End)
a(n) = 5 + 7^n - 2^(n+1) - 2*4^n. - Peter Kagey, Nov 15 2020
EXAMPLE
For n = 4, the 4-prism is the 3-dimensional cube, so a(4) = A334247(3) = 1862.
MATHEMATICA
A338153[n_] := 5 + 7^n - 2^(n + 1) - 2*4^n (* Peter Kagey, Nov 15 2020 *)
CROSSREFS
Cf. A033815 (cross-polytope), A058809 (wheel), A334247 (cube), A338152 (n-demihypercube), A338154 (n-antiprism).
Sequence in context: A154518 A249285 A292346 * A234796 A234789 A099105
KEYWORD
nonn
AUTHOR
Peter Kagey, Oct 13 2020
STATUS
approved