OFFSET
3,1
COMMENTS
Conjectured linear recurrence and g.f. confirmed by Kagey's formula. - Ray Chandler, Mar 10 2024
LINKS
Peter Kagey, Table of n, a(n) for n = 3..1000
Eric Weisstein's World of Mathematics, Antiprism Graph
Wikipedia, Acyclic orientation
Index entries for linear recurrences with constant coefficients, signature (17, -88, 153, -81).
FORMULA
Conjectures from Colin Barker, Oct 13 2020: (Start)
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)).
a(n) = 17*a(n-1) - 88*a(n-2) + 153*a(n-3) - 81*a(n-4) for n>6.
(End)
a(n) = -2^(1-n)*((7-sqrt(13))^n + (7+sqrt(13))^n) + 9^n + 5. - Peter Kagey, Nov 15 2020
EXAMPLE
For n = 3, the 3-antiprism is the octahedron (3-dimensional cross-polytope), so a(3) = A033815(3) = 426.
MATHEMATICA
A338154[n_] := Round[-2^(1-n)*((7 - Sqrt[13])^n + (7 + Sqrt[13])^n) + 9^n + 5] (* Peter Kagey, Nov 15 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Oct 13 2020
STATUS
approved