A354695 G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x)^3.

1, 1, 3, 6, 11, 21, 42, 87, 189, 432, 1018, 2415, 5694, 13297, 30768, 70626, 161011, 364977, 823536, 1851706, 4152972, 9298653, 20800758, 46516437, 104044590, 232856189, 521601174, 1169670645, 2626188319, 5904269526, 13292581605, 29968831278, 67663806228

Offset

0,3

Links

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

Formula

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

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, binomial(i+1, 3*j+2)*v[j+1])); v;

Crossrefs

Cf. A119685, A354696.

Cf. A351816, A352045.

Sequence in context: A293320 A024495 A360045 * A293066 A104253 A283668

Adjacent sequences: A354692 A354693 A354694 * A354696 A354697 A354698

Keyword

nonn

Author

Seiichi Manyama, Jun 03 2022

Status

approved