A346733 - OEIS

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A346733

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

1, 1, 1, 1, 3, 6, 10, 21, 48, 103, 219, 489, 1114, 2517, 5712, 13152, 30492, 70812, 165165, 387456, 912378, 2154250, 5102343, 12123027, 28878384, 68947041, 164979006, 395604531, 950428335, 2287387152, 5514240673, 13314167718, 32194109193, 77953239507, 188997294360

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

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..34.

FORMULA

a(0) = a(1) = a(2) = 1; a(n) = Sum_{i=0..n-3} Sum_{j=0..n-i-3} a(i) * a(j) * a(n-i-j-3).

MATHEMATICA

nmax = 34; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 A[x]^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[n_] := a[n] = If[n < 3, 1, Sum[Sum[a[i] a[j] a[n - i - j - 3], {j, 0, n - i - 3}], {i, 0, n - 3}]]; Table[a[n], {n, 0, 34}]

CROSSREFS

Cf. A001764, A019497, A307970, A346734, A346735.