A352879 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n,3*k+1) * a(k).

1, 1, 2, 3, 5, 10, 21, 44, 94, 207, 463, 1034, 2289, 5023, 10952, 23784, 51550, 111707, 242370, 527176, 1150643, 2522064, 5553977, 12290257, 27326784, 61031999, 136860175, 307979631, 695115874, 1572737222, 3565447689, 8095730133, 18405209484

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Formula

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

E.g.f.: 1 + exp(x) * Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)!.

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k + 1] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 32}]
nmax = 32; A[_] = 0; Do[A[x_] = 1 + x A[x^3/(1 - x)^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A040027, A119685, A352045, A352904.

Sequence in context: A131708 A002991 A218532 * A022861 A352818 A346970

Adjacent sequences: A352876 A352877 A352878 * A352880 A352881 A352882

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2022

Status

approved