A122973 Number of vertices on the surface of an icosahedron.

1, 12, 42, 162, 642, 2562, 10242, 40962, 163842, 655362, 2621442, 10485762, 41943042, 167772162, 671088642, 2684354562, 10737418242, 42949672962, 171798691842, 687194767362, 2748779069442, 10995116277762, 43980465111042, 175921860444162, 703687441776642

Offset: 0

Author

Alden Chew (aldenc98(AT)yahoo.com), Oct 27 2006

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A005901.

Programs

Mathematica

Join[{1},LinearRecurrence[{5,-4},{12,42},30]] (* or *) CoefficientList[ Series[1-6x (-2+3x)/((4x-1)(x-1)),{x,0,30}],x] (* Harvey P. Dale, May 05 2011 *)

Formula

a(n) = 1 if n=0, 10*4^(n-1)+2 otherwise.

G.f.: 1-6*x*(-2+3*x) / ( (4*x-1)*(x-1) ). - R. J. Mathar, Feb 02 2011

For a(n)>1: a(1)=12, a(2)=42, a(n) = 5*a(n-1)-4*a(n-2). [Harvey P. Dale, May 05 2011]