OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=1..ceiling((n+1)/3)} binomial(2*n-3*k+1,n-3*k+1)), n>0, a(0)=0.
G.f.: log'(1/(1-x^3*C(x)^3))/3, where C(x) is g.f. of A000108.
a(n) ~ 2^(2*n+1)/(7*sqrt(Pi*n)). - Vaclav Kotesovec, May 24 2014
Conjecture D-finite with recurrence: 3*(n+1)*a(n) -18*n*a(n-1) +2*(11*n-13)*a(n-2) +6*(n-7)*a(n-3) +(7*n-9)*a(n-4) +2*(2*n-7)*a(n-5)=0. - R. J. Mathar, Jan 25 2020
MATHEMATICA
CoefficientList[Series[(1-2*x-Sqrt[1-4*x])/(4*x^2+Sqrt[1-4*x]*(3*x+1)-5*x+1), {x, 0, 20}], x] (* Vaclav Kotesovec, May 24 2014 *)
PROG
(Maxima)
a(n):=sum(binomial(2*n-3*k+1, n-3*k+1), k, 1, ceiling((n+1)/3));
(PARI) x='x+O('x^50); concat([0, 0], Vec((1-2*x-sqrt(1-4*x))/(4*x^2 + sqrt(1-4*x)*(3*x+1)-5*x+1))) \\ G. C. Greubel, Jun 01 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, May 24 2014
STATUS
approved