A346734 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x)^3.

1, 1, 1, 1, 1, 3, 6, 10, 15, 27, 55, 111, 210, 388, 741, 1473, 2956, 5856, 11514, 22806, 45756, 92394, 186459, 375867, 759519, 1541803, 3140775, 6407307, 13081230, 26745378, 54797850, 112495734, 231270690, 475960278, 980643070, 2023057266, 4178837181, 8641346835

Offset

0,6

Links

Table of n, a(n) for n=0..37.

Formula

a(0) = ... = a(3) = 1; a(n) = Sum_{i=0..n-4} Sum_{j=0..n-i-4} a(i) * a(j) * a(n-i-j-4).

Mathematica

nmax = 37; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 A[x]^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = If[n < 4, 1, Sum[Sum[a[i] a[j] a[n - i - j - 4], {j, 0, n - i - 4}], {i, 0, n - 4}]]; Table[a[n], {n, 0, 37}]

Crossrefs

Cf. A001764, A019497, A307971, A346733, A346735.

Sequence in context: A058576 A360893 A365696 * A366132 A230364 A214282

Adjacent sequences: A346731 A346732 A346733 * A346735 A346736 A346737

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 30 2021

Status

approved