OFFSET
0,9
FORMULA
a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,n-4*k) * binomial(n-2*k+1,k) / (n-2*k+1).
From Vaclav Kotesovec, Sep 26 2023: (Start)
G.f.: (1 + x - sqrt(1 - 2*x + x^2 - 4*x^4)) / (2*x*(1 + x^3)).
a(n) ~ 2^(n + 3/2) / (sqrt(Pi) * 3^(3/2) * n^(3/2)). (End)
MATHEMATICA
CoefficientList[Series[(1 + x - Sqrt[1 - 2*x + x^2 - 4*x^4])/(2*x*(1 + x^3)), {x, 0, 40}], x] (* Vaclav Kotesovec, Sep 26 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(n-3*k-1, n-4*k)*binomial(n-2*k+1, k)/(n-2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 16 2023
STATUS
approved