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