A357308 a(0) = a(1) = 0, a(2) = 1; a(n) = a(n-1) + Sum_{k=0..n-3} a(k) * a(n-k-3).

0, 0, 1, 1, 1, 1, 1, 2, 4, 7, 11, 16, 24, 39, 67, 116, 196, 324, 534, 892, 1516, 2601, 4463, 7630, 13022, 22276, 38286, 66084, 114328, 197929, 342783, 594218, 1031794, 1794944, 3127450, 5455272, 9523812, 16640542, 29102938, 50951070, 89289998, 156616648, 274923328, 482945930, 848972814

Offset

0,8

Links

Table of n, a(n) for n=0..44.

Formula

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

Mathematica

a[0] = a[1] = 0; a[2] = 1; a[n_] := a[n] = a[n - 1] + Sum[a[k] a[n - k - 3], {k, 0, n - 3}]; Table[a[n], {n, 0, 44}]
nmax = 44; A[_] = 0; Do[A[x_] = x^2 (1 + x A[x]^2)/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A006318, A023426, A023431, A025246, A346503, A346504, A357307.

Sequence in context: A063676 A099385 A331387 * A357933 A237821 A120118

Adjacent sequences: A357305 A357306 A357307 * A357309 A357310 A357311

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 23 2022

Status

approved