A357307 a(0) = 1, a(1) = 0, a(2) = 1; a(n) = a(n-1) + Sum_{k=0..n-3} a(k) * a(n-k-3).

1, 0, 1, 2, 2, 4, 8, 13, 25, 49, 91, 177, 349, 681, 1349, 2693, 5377, 10806, 21820, 44163, 89721, 182868, 373616, 765341, 1571551, 3233690, 6667242, 13772469, 28498419, 59065838, 122606998, 254865837, 530507839, 1105663034, 2307131590, 4819623077, 10079039819, 21099213611, 44211213545

Offset

0,4

Links

Table of n, a(n) for n=0..38.

Formula

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

Mathematica

a[0] = 1; 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, 38}]
nmax = 38; A[_] = 0; Do[A[x_] = 1 + x^2 (1 + x A[x]^2)/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000245, A023426, A023431, A090345, A346503, A346504, A357308.

Sequence in context: A036761 A042979 A000018 * A306604 A354784 A075126

Adjacent sequences: A357304 A357305 A357306 * A357308 A357309 A357310

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 23 2022

Status

approved