OFFSET
0,1
COMMENTS
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.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (4,-3).
FORMULA
a(n) = 2*3^n + 2.
From Colin Barker, May 31 2016: (Start)
a(n) = 4*a(n-1)-3*a(n-2) for n>1.
G.f.: 4*(1-2*x) / ((1-x)*(1-3*x)).
(End)
E.g.f.: 2*(1 + exp(2*x))*exp(x). - Ilya Gutkovskiy, May 31 2016
a(n) = 4 * A007051(n). - Alois P. Heinz, Jun 26 2023
MAPLE
seq(2*3^i+2, i=0..30);
MATHEMATICA
a=4; lst={a}; Do[a=a*3-4; AppendTo[lst, a], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)
PROG
(Magma) [2*3^n+2: n in [0..30]]; // Vincenzo Librandi, Jun 05 2011
(PARI) Vec(4*(1-2*x)/((1-x)*(1-3*x)) + O(x^30)) \\ Colin Barker, May 31 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Miklos Kristof, Mar 02 2006
STATUS
approved