OFFSET
0,1
COMMENTS
1/2 + 1/16 + 1/128 + 1/1024 + ... = 4/7. - Gary W. Adamson, Aug 29 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (8).
FORMULA
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 8*a(n-1), n > 0; a(0)=2.
G.f.: 2/(1-8x). (End)
From Amiram Eldar, May 08 2023: (Start)
Sum_{n>=0} (-1)^n/a(n) = 4/9.
Product_{n>=0} (1 - 1/a(n)) = A132024. (End)
E.g.f.: 2*exp(8*x). - Stefano Spezia, May 29 2024
MAPLE
seq(2^(3*n+1), n=0..19); # Nathaniel Johnston, Jun 26 2011
MATHEMATICA
Table[2^n, {n, 1, 100, 3}] (* and *) 2^(3*Range[0, 40] + 1) (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
PROG
(Magma) [2^(3*n+1): n in [0..30]]; // Vincenzo Librandi, May 04 2011
(PARI) a(n)=2<<(3*n) \\ Charles R Greathouse IV, Jun 14 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved