OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (16,-64).
FORMULA
a(n) = 16*a(n-1)-64*a(n-2).
G.f.: (1+8*x)/(1-8*x)^2.
a(n) = 8*(a(n-1)+2^(3*n-2)). - Vincenzo Librandi, Nov 05 2011
From Amiram Eldar, Dec 10 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(8)*arccoth(sqrt(8)).
Sum_{n>=0} (-1)^n/a(n) = sqrt(8)*arccot(sqrt(8)). (End)
E.g.f.: exp(8*x)*(1 + 16*x). - Stefano Spezia, May 09 2023
MAPLE
MATHEMATICA
Table[(2 n + 1)*8^n, {n, 0, 20}] (* Wesley Ivan Hurt, Oct 30 2014 *)
PROG
(Magma) [(2*n+1)*8^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011
(PARI) a(n) = (2*n+1)*8^n \\ Amiram Eldar, Dec 10 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Nov 04 2011
EXTENSIONS
a(18) corrected by Vincenzo Librandi, Nov 05 2011
STATUS
approved