OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: (1-sqrt((1-4*x-2*x^2)/(1-2*x^2)))/(2*x).
a(n) = Sum_{k=0..floor(n/2)} 2^k*C(n-k,k)*C(n-2*k).
Conjecture: (n+1)*a(n) +2(1-2n)*a(n-1) +4*(1-n)*a(n-2) +4*(2n-3)*a(n-3) +4*(n-3)*a(n-4)=0. - R. J. Mathar, Dec 13 2011
a(n) ~ 3^(1/4) * (2+sqrt(6))^(n+1) / (2^(9/4) * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 01 2014
G.f.: 1/G(x), with G(x) = 1-2*x^2-(x-x^3)/(1-x^2-(x-x^3)/G(x)) (continued fraction). - Nikolaos Pantelidis, Jan 09 2023
MATHEMATICA
CoefficientList[Series[(1-Sqrt[(1-4*x-2*x^2)/(1-2*x^2)])/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)
PROG
(PARI) x='x+O('x^50); Vec((1-sqrt((1-4*x-2*x^2)/(1-2*x^2)))/(2*x)) \\ G. C. Greubel, Mar 16 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 23 2005
STATUS
approved