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
Examples
n = 1 is the icosahedron with 30 sides. After dividing each face in 4, there are 120 sides in the next iteration.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4).
Programs
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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 *) -
PARI
Vec((1+26*x)/(1-4*x) + O(x^30)) \\ Colin Barker, Oct 20 2016
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Python
a = [1] + [30 * 4 ** (n-1) for n in range(1,24)]
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)
Comments