OFFSET
0,1
COMMENTS
The partial sums of A001246(n)/a(n) converge absolutely. This series is also the hypergeometric function 1/4 * 4F3(1/2,1/2,1,1;2,2,2;1). - Ralf Steiner, Feb 09 2016
LINKS
Colin Barker, Table of n, a(n) for n = 0..800
Index entries for linear recurrences with constant coefficients, signature (32,-256).
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)
EXAMPLE
For n=3, a(3) = (3+1)*4^(2*3+1) = 4*4^7 = 65536.
MATHEMATICA
Table[(n + 1) 4^(2 n + 1), {n, 0, 20}] (* Vincenzo Librandi, Feb 10 2016 *)
PROG
(PARI) a(n) = (n+1)*4^(2*n+1); \\ Michel Marcus, Jan 28 2016
(PARI) Vec(4 / (1 - 16*x)^2 + O(x^30)) \\ Colin Barker, Mar 23 2017
(Magma) [(n+1)*4^(2*n+1): n in [0..45]]; // Vincenzo Librandi, Feb 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Steiner, Jan 24 2016
EXTENSIONS
More terms from Michel Marcus, Jan 28 2016
STATUS
approved