A205646 Number of empty faces in Freij's family of Hansen polytopes.

17, 19, 25, 43, 97, 259, 745, 2203, 6577, 19699, 59065, 177163, 531457, 1594339, 4782985, 14348923, 43046737, 129140179, 387420505, 1162261483, 3486784417, 10460353219, 31381059625, 94143178843, 282429536497, 847288609459, 2541865828345, 7625597485003

Offset: 0

Author

Jonathan Vos Post, Jan 29 2012

Keywords

• nonn
• easy

Comments

Freij's study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.

Examples

			a(4) = (3^4) + 16 = 97.
		

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).

Crossrefs

Cf. A000244 (powers of 3), A205647.

Programs

Mathematica

3^Range[0,30]+16 (* Paolo Xausa, Oct 24 2023 *)

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)

Extensions

Terms corrected by Colin Barker, May 02 2013