A343305 - OEIS

A343305

a(0) = ... = a(3) = 1; a(n) = a(n-4) + Sum_{k=0..n-5} a(k) * a(n-k-5).

1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 11, 17, 25, 36, 53, 81, 125, 191, 289, 439, 675, 1046, 1621, 2506, 3877, 6023, 9395, 14681, 22947, 35890, 56231, 88285, 138825, 218493, 344145, 542618, 856597, 1353766, 2141383, 3389797, 5370219, 8514773, 13511673, 21456808, 34096503, 54216636

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..45.

FORMULA

G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x) + x^5 * A(x)^2.

MATHEMATICA

a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[n - 4] + Sum[a[k] a[n - k - 5], {k, 0, n - 5}]; Table[a[n], {n, 0, 45}]

nmax = 45; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 A[x] + x^5 A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

CROSSREFS

Cf. A001006, A050253, A307972, A343304.