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

%I A277451 #21 Nov 15 2016 06:58:01
%S A277451 1,30,120,480,1920,7680,30720,122880,491520,1966080,7864320,31457280,
%T A277451 125829120,503316480,2013265920,8053063680,32212254720,128849018880,
%U A277451 515396075520,2061584302080,8246337208320,32985348833280,131941395333120,527765581332480
%N A277451 Number of edges in geodesic dome generated from icosahedron by recursively dividing each triangle in 4.
%C A277451 The new triangles are generated by placing new vertices at the midpoints of each edge in the old triangle.
%H A277451 Colin Barker, <a href="/A277451/b277451.txt">Table of n, a(n) for n = 0..1000</a>
%H A277451 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (4).
%F A277451 a(n) = 1 if n=0, else 30*4^(n-1).
%F A277451 From _Colin Barker_, Oct 20 2016: (Start)
%F A277451 a(n) = 4*a(n-1) for n>1.
%F A277451 G.f.: (1+26*x) / (1-4*x). (End)
%e A277451 n = 1 is the icosahedron with 30 sides. After dividing each face in 4, there are 120 sides in the next iteration.
%t A277451 {1}~Join~NestList[4 # &, 30, 22] (* or *)
%t A277451 CoefficientList[Series[(1 + 26 x)/(1 - 4 x), {x, 0, 23}], x] (* _Michael De Vlieger_, Oct 21 2016 *)
%o A277451 (Python) a = [1] + [30 * 4 ** (n-1) for n in range(1,24)]
%o A277451 (PARI) Vec((1+26*x)/(1-4*x) + O(x^30)) \\ _Colin Barker_, Oct 20 2016
%Y A277451 A122973 is the number of vertices, A003947 is the number of faces starting from 20.
%K A277451 nonn,easy
%O A277451 0,2
%A A277451 _Jonah Caplan_, Oct 16 2016