cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A205646 #31 Nov 09 2023 11:05:54
%S A205646 17,19,25,43,97,259,745,2203,6577,19699,59065,177163,531457,1594339,
%T A205646 4782985,14348923,43046737,129140179,387420505,1162261483,3486784417,
%U A205646 10460353219,31381059625,94143178843,282429536497,847288609459,2541865828345,7625597485003
%N A205646 Number of empty faces in Freij's family of Hansen polytopes.
%C A205646 Freij's study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.
%H A205646 Paolo Xausa, <a href="/A205646/b205646.txt">Table of n, a(n) for n = 0..1000</a>
%H A205646 Ragnar Freij, Matthias Henze, Moritz W. Schmitt, and Günter M. Ziegler, <a href="http://arxiv.org/abs/1201.5790">Face numbers of centrally symmetric polytopes from split graphs</a>, arXiv:1201.5790 [math.MG], 2012.
%H A205646 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A205646 a(n) = 3^n + 16.
%F A205646 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
%F A205646 From _Elmo R. Oliveira_, Nov 09 2023: (Start)
%F A205646 a(n) = 3*a(n-1) - 32 with a(0) = 17.
%F A205646 E.g.f.: exp(3*x) + 16*exp(x). (End)
%e A205646 a(4) = (3^4) + 16 = 97.
%t A205646 3^Range[0,30]+16 (* _Paolo Xausa_, Oct 24 2023 *)
%Y A205646 Cf. A000244 (powers of 3), A205647.
%K A205646 nonn,easy
%O A205646 0,1
%A A205646 _Jonathan Vos Post_, Jan 29 2012
%E A205646 Terms corrected by _Colin Barker_, May 02 2013