%I #23 Jun 26 2023 19:32:32
%S 4,8,20,56,164,488,1460,4376,13124,39368,118100,354296,1062884,
%T 3188648,9565940,28697816,86093444,258280328,774840980,2324522936,
%U 6973568804,20920706408,62762119220,188286357656,564859072964,1694577218888,5083731656660,15251194969976
%N a(0)=4, a(n) = 3*a(n-1) - 4.
%C A tetrahedron has 4 faces. Cut every corner so that we get triangular faces; the resulting polyhedron has 8 faces. Repeating this procedure gives polyhedra with 4, 8, 20, 56, etc. faces.
%H Vincenzo Librandi, <a href="/A115099/b115099.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F a(n) = 2*3^n + 2.
%F From _Colin Barker_, May 31 2016: (Start)
%F a(n) = 4*a(n-1)-3*a(n-2) for n>1.
%F G.f.: 4*(1-2*x) / ((1-x)*(1-3*x)).
%F (End)
%F E.g.f.: 2*(1 + exp(2*x))*exp(x). - _Ilya Gutkovskiy_, May 31 2016
%F a(n) = 4 * A007051(n). - _Alois P. Heinz_, Jun 26 2023
%p seq(2*3^i+2,i=0..30);
%t a=4;lst={a};Do[a=a*3-4;AppendTo[lst,a],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008 *)
%o (Magma) [2*3^n+2: n in [0..30]]; // _Vincenzo Librandi_, Jun 05 2011
%o (PARI) Vec(4*(1-2*x)/((1-x)*(1-3*x)) + O(x^30)) \\ _Colin Barker_, May 31 2016
%Y Cf. A003462, A007051, A034472, A024023, A067771, A029858, A134931. - _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008
%K easy,nonn
%O 0,1
%A _Miklos Kristof_, Mar 02 2006