OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
G.f.: (1+2*x)/(4*x*sqrt(1-4*x-4*x^2))-1/(4*x);
a(n) = Sum_{k=0..n} 2^(n-k)*C(n,k)*C(k,floor(k/2))2^floor(k/2).
D-finite with recurrence: (n+1)*a(n) -2*(n+2)*a(n-1) +12*(1-n)*a(n-2) +8*(2-n)*a(n-3) = 0. - R. J. Mathar, Dec 10 2011
Shorter recurrence: n*(n+1)*a(n) = 2*n*(2*n+1)*a(n-1) + 4*(n-1)*(n+1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012
a(n) ~ sqrt(20+14*sqrt(2))*(2+2*sqrt(2))^n/(4*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 19 2012
MATHEMATICA
CoefficientList[Series[(1+2*x)/(4*x*Sqrt[1-4*x-4*x^2])-1/(4*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)
PROG
(PARI) x='x+O('x^50); Vec((1+2*x)/(4*x*sqrt(1-4*x-4*x^2))-1/(4*x)) \\ G. C. Greubel, Feb 08 2017
(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1+2*x)/(4*x*Sqrt(1-4*x-4*x^2)) -1/(4*x))); // G. C. Greubel, Aug 17 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 02 2006
STATUS
approved