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

0,2

Links

Table of n, a(n) for n=0..24.

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

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]

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 *)

Crossrefs

Cf. A005901.

Sequence in context: A007586 A228391 A334277 * A074356 A172294 A238225

Adjacent sequences: A122970 A122971 A122972 * A122974 A122975 A122976

Keyword

nonn,easy

Author

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

Status

approved