OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = a(n-1) + Sum_{j=0..n-2} A217312(j)*a(n-j).
G.f: 1/(1-x-x^2(1/(1-x-x^2*R(x)))), where R(x) is the g.f. of Riordan numbers (A005043).
a(n) ~ 3^(n+3/2) / (32*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 21 2015
Conjecture: (-n+3)*a(n) +3*(2*n-7)*a(n-1) +(-7*n+24)*a(n-2) +2*(-7*n+36)*a(n-3) +2*(11*n-51)*a(n-4) +3*(3*n-23)*a(n-5) +(-10*n+63)*a(n-6) +3*(n-6)*a(n-7)=0. - R. J. Mathar, Sep 24 2016
MATHEMATICA
CoefficientList[Series[1/(1-x-x^2(1/(1-x-x^2*(1+x-Sqrt[1-2*x-3*x^2])/(2*x*(1+x))))), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 21 2015 *)
PROG
(PARI) x='x + O('x^50); Vec(1/(1-x-x^2*(1/(1-x-x^2*(1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)))))) \\ G. C. Greubel, Feb 14 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
José Luis Ramírez Ramírez, Apr 20 2015
STATUS
approved