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A338153 a(n) is the number of acyclic orientations of the edges of the n-prism.

%I A338153 #22 Mar 10 2024 18:27:41
%S A338153 204,1862,14700,109334,790524,5633222,39828300,280376054,1968934044,
%T A338153 13807724582,96754776300,677686169174,4745413960764,33224340503942,
%U A338153 232596153986700,1628276158432694,11398345428510684,79790067272259302,558537067986067500,3909785864202510614
%N A338153 a(n) is the number of acyclic orientations of the edges of the n-prism.
%C A338153 Conjectured linear recurrence and g.f. confirmed by Kagey's formula. - _Ray Chandler_, Mar 10 2024
%H A338153 Peter Kagey, <a href="/A338153/b338153.txt">Table of n, a(n) for n = 3..1000</a>
%H A338153 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H A338153 Wikipedia, <a href="https://en.wikipedia.org/wiki/Acyclic_orientation">Acyclic orientation</a>
%H A338153 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (14, -63, 106, -56).
%F A338153 Conjectures from _Colin Barker_, Oct 13 2020: (Start)
%F A338153 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)).
%F A338153 a(n) = 14*a(n-1) - 63*a(n-2) + 106*a(n-3) - 56*a(n-4) for n>6.
%F A338153 (End)
%F A338153 a(n) = 5 + 7^n - 2^(n+1) - 2*4^n. - _Peter Kagey_, Nov 15 2020
%e A338153 For n = 4, the 4-prism is the 3-dimensional cube, so a(4) = A334247(3) = 1862.
%t A338153 A338153[n_] := 5 + 7^n - 2^(n + 1) - 2*4^n (* _Peter Kagey_, Nov 15 2020 *)
%Y A338153 Cf. A102080, A124349, A284702.
%Y A338153 Cf. A033815 (cross-polytope), A058809 (wheel), A334247 (cube), A338152 (n-demihypercube), A338154 (n-antiprism).
%K A338153 nonn
%O A338153 3,1
%A A338153 _Peter Kagey_, Oct 13 2020