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, Prism Graph
Wikipedia, Acyclic orientation
Index entries for linear recurrences with constant coefficients, signature (14, -63, 106, -56).
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
KEYWORD
nonn
AUTHOR
Peter Kagey, Oct 13 2020
STATUS
approved