A346735 - OEIS

A346735

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

1, 1, 1, 1, 1, 1, 3, 6, 10, 15, 21, 34, 63, 120, 220, 381, 642, 1102, 1968, 3615, 6658, 12090, 21675, 38820, 70200, 128466, 236583, 435453, 798798, 1462933, 2684352, 4945740, 9145839, 16942356, 31388571, 58140726, 107753364, 199993359, 371852269, 692375844, 1290252474

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,7

LINKS

Table of n, a(n) for n=0..40.

FORMULA

a(0) = ... = a(4) = 1; a(n) = Sum_{i=0..n-5} Sum_{j=0..n-i-5} a(i) * a(j) * a(n-i-j-5).

MATHEMATICA

nmax = 40; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 A[x]^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[n_] := a[n] = If[n < 5, 1, Sum[Sum[a[i] a[j] a[n - i - j - 5], {j, 0, n - i - 5}], {i, 0, n - 5}]]; Table[a[n], {n, 0, 40}]

CROSSREFS

Cf. A001764, A019497, A307972, A346733, A346734.