A352043 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-3*k-1,k) * a(k).

1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 50, 69, 95, 131, 181, 250, 346, 482, 678, 963, 1380, 1994, 2903, 4252, 6254, 9222, 13616, 20109, 29681, 43755, 64394, 94583, 138632, 202755, 295906, 430986, 626585, 909500, 1318384, 1909042, 2762122, 3994290

Offset: 0

Author

Ilya Gutkovskiy, Mar 01 2022

Keywords

• nonn

Crossrefs

Cf. A119262, A352042.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 3 k - 1, k] a[k], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 46}]
nmax = 46; A[] = 0; Do[A[x] = 1 + 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) = 1 + x * A(x^4/(1 - x)) / (1 - x).