OFFSET
0,1
COMMENTS
Freij's study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Ragnar Freij, Matthias Henze, Moritz W. Schmitt, and Günter M. Ziegler, Face numbers of centrally symmetric polytopes from split graphs, arXiv:1201.5790 [math.MG], 2012.
Index entries for linear recurrences with constant coefficients, signature (4,-3).
FORMULA
a(n) = 3^n + 16.
a(n) = 4*a(n-1) - 3*a(n-2). G.f.: (17 - 49*x) / ((1 - x)*(1 - 3*x)). - Colin Barker, May 02 2013
From Elmo R. Oliveira, Nov 09 2023: (Start)
a(n) = 3*a(n-1) - 32 with a(0) = 17.
E.g.f.: exp(3*x) + 16*exp(x). (End)
EXAMPLE
a(4) = (3^4) + 16 = 97.
MATHEMATICA
3^Range[0, 30]+16 (* Paolo Xausa, Oct 24 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Jan 29 2012
EXTENSIONS
Terms corrected by Colin Barker, May 02 2013
STATUS
approved