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%I #29 Mar 10 2024 18:22:53
%S 426,4968,50640,486930,4547088,41796168,380789562,3451622904,
%T 31194607488,281440825122,2536622917920,22848990484344,
%U 205743704494026,1852238413383048,16673036119790640,150072652217086770,1350735146332489008,12157047307392618408
%N a(n) is the number of acyclic orientations of the edges of the n-antiprism.
%C Conjectured linear recurrence and g.f. confirmed by Kagey's formula. - _Ray Chandler_, Mar 10 2024
%H Peter Kagey, <a href="/A338154/b338154.txt">Table of n, a(n) for n = 3..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Acyclic_orientation">Acyclic orientation</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (17, -88, 153, -81).
%F Conjectures from _Colin Barker_, Oct 13 2020: (Start)
%F G.f.: 6*x^3*(71 - 379*x + 612*x^2 - 324*x^3) / ((1 - x)*(1 - 9*x)*(1 - 7*x + 9*x^2)).
%F a(n) = 17*a(n-1) - 88*a(n-2) + 153*a(n-3) - 81*a(n-4) for n>6.
%F (End)
%F a(n) = -2^(1-n)*((7-sqrt(13))^n + (7+sqrt(13))^n) + 9^n + 5. - _Peter Kagey_, Nov 15 2020
%e For n = 3, the 3-antiprism is the octahedron (3-dimensional cross-polytope), so a(3) = A033815(3) = 426.
%t A338154[n_] := Round[-2^(1-n)*((7 - Sqrt[13])^n + (7 + Sqrt[13])^n) + 9^n + 5] (* _Peter Kagey_, Nov 15 2020 *)
%Y Cf. A077263, A124352, A124353, A192742, A284699, A284700, A284701, A287988, A294152, A297384.
%Y Cf. A033815 (cross-polytope), A058809 (wheel), A334247 (hypercube), A338152 (demihypercube), A338153 (prism).
%K nonn
%O 3,1
%A _Peter Kagey_, Oct 13 2020
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