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

0,1

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

Cf. A000244 (powers of 3), A205647.

Sequence in context: A226684 A334287 A249566 * A281192 A073247 A133347

Adjacent sequences: A205643 A205644 A205645 * A205647 A205648 A205649

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 29 2012

Extensions

Terms corrected by Colin Barker, May 02 2013

Status

approved