A360892 G.f. satisfies A(x) = 1 + x/(1 - x^3)^2 * A(x/(1 - x^3)).

1, 1, 1, 1, 3, 6, 10, 18, 42, 94, 193, 428, 1036, 2470, 5779, 14192, 36176, 91649, 233617, 613978, 1641492, 4396393, 11922501, 32969768, 92080274, 258774392, 736441673, 2123145058, 6168831095, 18067587851, 53493963264, 159884523503, 481343585105, 1461055679181

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-2*k,k) * a(n-1-3*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-2*j, j)*v[i-3*j])); v;

Crossrefs

Cf. A040027, A352864, A360893.

Cf. A360890, A360900.

Sequence in context: A075111 A080014 A364403 * A132274 A253768 A091714

Adjacent sequences: A360889 A360890 A360891 * A360893 A360894 A360895

Keyword

nonn

Author

Seiichi Manyama, Feb 25 2023

Status

approved