A277451 Number of edges in geodesic dome generated from icosahedron by recursively dividing each triangle in 4.

1, 30, 120, 480, 1920, 7680, 30720, 122880, 491520, 1966080, 7864320, 31457280, 125829120, 503316480, 2013265920, 8053063680, 32212254720, 128849018880, 515396075520, 2061584302080, 8246337208320, 32985348833280, 131941395333120, 527765581332480

Offset

0,2

Comments

The new triangles are generated by placing new vertices at the midpoints of each edge in the old triangle.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 1 if n=0, else 30*4^(n-1).

From Colin Barker, Oct 20 2016: (Start)

a(n) = 4*a(n-1) for n>1.

G.f.: (1+26*x) / (1-4*x). (End)

Example

n = 1 is the icosahedron with 30 sides. After dividing each face in 4, there are 120 sides in the next iteration.

Mathematica

{1}~Join~NestList[4 # &, 30, 22] (* or *)
CoefficientList[Series[(1 + 26 x)/(1 - 4 x), {x, 0, 23}], x] (* Michael De Vlieger, Oct 21 2016 *)

Prog

(Python) a = [1] + [30 * 4 ** (n-1) for n in range(1, 24)]
(PARI) Vec((1+26*x)/(1-4*x) + O(x^30)) \\ Colin Barker, Oct 20 2016

Crossrefs

A122973 is the number of vertices, A003947 is the number of faces starting from 20.

Sequence in context: A112955 A244636 A290391 * A042764 A219223 A042766

Adjacent sequences: A277448 A277449 A277450 * A277452 A277453 A277454

Keyword

nonn,easy

Author

Jonah Caplan, Oct 16 2016

Status

approved