OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2).
FORMULA
From Bruno Berselli, Mar 02 2011: (Start)
G.f.: 3*(3+5*x)/(1-2*x^2).
a(n) = 3*(4-(-1)^n)*2^((2*n+(-1)^n-1)/4). Therefore: a(n) = 9*2^(n/2) for n even, otherwise a(n) = 15*2^((n-1)/2).
a(n) = 2*a(n-2) for n>1. (End)
Sum_{n>=0} 1/a(n) = 16/45. - Amiram Eldar, Mar 28 2022
MATHEMATICA
a = {}; Do[a = Append[a, FromDigits[ Join[{1, 0, 0, 1}, Table[0, {n}]], 2]]; a = Append[a, FromDigits[ Join[{1, 1, 1, 1}, Table[0, {n}]], 2]], {n, 0, 20}]; a
CoefficientList[Series[3 (3 + 5 x) / (1 - 2 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{0, 2}, {9, 15}, 40] (* Harvey P. Dale, Aug 06 2021 *)
PROG
(Magma) [n le 2 select 6*n+3 else 2*Self(n-2): n in [1..38]]; // Bruno Berselli, Mar 02 2011
(PARI) my(x='x+O('x^99)); Vec(3*(3+5*x)/(1-2*x^2)) \\ Altug Alkan, Sep 20 2018
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, May 19 2002
EXTENSIONS
More terms from Robert G. Wilson v, May 20 2002
STATUS
approved