A346048 a(0) = ... = a(3) = 1; a(n) = Sum_{k=1..n-4} a(k) * a(n-k-4).

1, 1, 1, 1, 0, 1, 2, 3, 3, 3, 5, 9, 15, 19, 24, 35, 59, 95, 137, 191, 280, 445, 706, 1071, 1575, 2357, 3663, 5755, 8890, 13483, 20518, 31759, 49658, 77267, 119135, 183523, 284793, 444883, 694798, 1080865, 1679142, 2616399, 4092497, 6408249, 10021176, 15657643

Offset

0,7

Links

Table of n, a(n) for n=0..45.

Formula

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

Maple

a:= proc(n) option remember; `if`(n<4, 1,
      add(a(j)*a(n-4-j), j=1..n-4))
    end:
seq(a(n), n=0..45);  # Alois P. Heinz, Jul 03 2021

Mathematica

a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = Sum[a[k] a[n - k - 4], {k, 1, n - 4}]; Table[a[n], {n, 0, 45}]
nmax = 45; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A025250, A307971, A343304, A343305, A346047, A346049.

Sequence in context: A341074 A343885 A264870 * A131048 A119688 A126868

Adjacent sequences: A346045 A346046 A346047 * A346049 A346050 A346051

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 02 2021

Status

approved