A344491 a(n) = 1 + Sum_{k=0..n-4} binomial(n-3,k) * a(k).

1, 1, 1, 1, 2, 4, 8, 16, 37, 97, 275, 810, 2468, 7840, 26182, 92047, 339029, 1299185, 5152244, 21091816, 89087652, 388318264, 1746324563, 8094422821, 38608318847, 189179752492, 950930369320, 4898477508796, 25841317224002, 139534769647745, 770795537345237, 4353368099507329

Offset

0,5

Links

Table of n, a(n) for n=0..31.

Formula

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

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n - 3, k] a[k] , {k, 0, n - 4}]; Table[a[n], {n, 0, 31}]
nmax = 31; A[_] = 0; Do[A[x_] = (1 + x^3 A[x/(1 - x)])/((1 - x) (1 + x^3)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000629, A210541, A344489, A344490, A344492, A344493.

Sequence in context: A018536 A337673 A162428 * A028497 A197244 A350495

Adjacent sequences: A344488 A344489 A344490 * A344492 A344493 A344494

Keyword

nonn

Author

Ilya Gutkovskiy, May 21 2021

Status

approved