A343304 a(0) = a(1) = a(2) = 1; a(n) = a(n-3) + Sum_{k=0..n-4} a(k) * a(n-k-4).

1, 1, 1, 1, 2, 3, 4, 6, 10, 16, 25, 40, 66, 109, 179, 296, 495, 831, 1396, 2353, 3985, 6770, 11523, 19657, 33621, 57633, 98969, 170245, 293371, 506371, 875284, 1515029, 2625842, 4556806, 7916943, 13769900, 23975073, 41785251, 72894759, 127279673, 222430235, 389030773, 680946436, 1192794189

Offset

0,5

Links

Table of n, a(n) for n=0..43.

Formula

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

Mathematica

a[0] = a[1] = a[2] = 1; a[n_] := a[n] = a[n - 3] + Sum[a[k] a[n - k - 4], {k, 0, n - 4}]; Table[a[n], {n, 0, 43}]
nmax = 43; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 A[x] + x^4 A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A001006, A050253, A307971, A343305.

Sequence in context: A018142 A173697 A017986 * A346075 A352946 A342759

Adjacent sequences: A343301 A343302 A343303 * A343305 A343306 A343307

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 11 2021

Status

approved