A267796 a(n) = (n+1)*4^(2n+1).
4, 128, 3072, 65536, 1310720, 25165824, 469762048, 8589934592, 154618822656, 2748779069440, 48378511622144, 844424930131968, 14636698788954112, 252201579132747776, 4323455642275676160, 73786976294838206464, 1254378597012249509888, 21250649172913403461632
Offset: 0
Examples
For n=3, a(3) = (3+1)*4^(2*3+1) = 4*4^7 = 65536.
Links
- Colin Barker, Table of n, a(n) for n = 0..800
- Index entries for linear recurrences with constant coefficients, signature (32,-256).
Programs
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Magma
[(n+1)*4^(2*n+1): n in [0..45]]; // Vincenzo Librandi, Feb 10 2016
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Mathematica
Table[(n + 1) 4^(2 n + 1), {n, 0, 20}] (* Vincenzo Librandi, Feb 10 2016 *) -
PARI
a(n) = (n+1)*4^(2*n+1); \\ Michel Marcus, Jan 28 2016
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PARI
Vec(4 / (1 - 16*x)^2 + O(x^30)) \\ Colin Barker, Mar 23 2017
Formula
a(n) = A013709(n)*(n+1).
From Colin Barker, Mar 23 2017: (Start)
G.f.: 4 / (1 - 16*x)^2.
a(n) = 32*a(n-1) - 256*a(n-2) for n>1. (End)
From Amiram Eldar, Apr 17 2022: (Start)
a(n) = A193132(n+1)/3.
Sum_{n>=0} 1/a(n) = 4*log(16/15).
Sum_{n>=0} (-1)^n/a(n) = 4*log(17/16). (End)
Extensions
More terms from Michel Marcus, Jan 28 2016
Comments