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G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x)^3.
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%I #6 Jul 31 2021 09:44:05

%S 1,1,1,1,1,1,3,6,10,15,21,34,63,120,220,381,642,1102,1968,3615,6658,

%T 12090,21675,38820,70200,128466,236583,435453,798798,1462933,2684352,

%U 4945740,9145839,16942356,31388571,58140726,107753364,199993359,371852269,692375844,1290252474

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

%F 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).

%t 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]

%t 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}]

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

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Jul 30 2021