A352041 a(0) = 1; a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * a(k).

1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 50, 69, 96, 136, 196, 285, 417, 614, 909, 1349, 2002, 2968, 4394, 6493, 9572, 14074, 20639, 30189, 44049, 64123, 93151, 135080, 195599, 282915, 408884, 590658, 853080, 1232168, 1780190, 2573059, 3721103

Offset: 0

Author

Ilya Gutkovskiy, Mar 01 2022

Keywords

• nonn

Crossrefs

Cf. A092684, A180184, A352039.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 3 k, k] a[k], {k, 0, Floor[n/4]}]; Table[a[n], {n, 0, 44}]
nmax = 44; A[] = 1; Do[A[x] = A[x^4/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = A(x^4/(1 - x)) / (1 - x).