A352045 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(k).

1, 1, 1, 1, 2, 5, 11, 22, 43, 85, 170, 341, 683, 1367, 2744, 5552, 11381, 23729, 50423, 109220, 240845, 539411, 1223357, 2800535, 6451340, 14915084, 34533851, 79949741, 184865936, 426627122, 982217705, 2255539406, 5166125852, 11802977573, 26903285366

Offset: 0

Author

Ilya Gutkovskiy, Mar 01 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A351970, A352044.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 3 k] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 34}]
nmax = 34; A[] = 0; Do[A[x] = 1 + x A[x^3/(1 - x)^3]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x).

E.g.f.: Integral exp(x) * Sum_{n>=0} a(n) * x^(3*n) / (3*n)! dx.