A360889 G.f. satisfies A(x) = 1 + x * (1 + x^3)^2 * A(x * (1 + x^3)).

1, 1, 1, 1, 3, 6, 10, 16, 37, 85, 175, 365, 865, 2090, 4826, 11447, 28797, 73086, 183422, 471462, 1249792, 3329832, 8898534, 24244771, 67210802, 187336493, 526399475, 1501301887, 4329346255, 12565028776, 36807317140, 109047854266, 325773015735, 980062229742

Offset

0,5

Links

Table of n, a(n) for n=0..33.

Formula

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

Crossrefs

Cf. A360887, A360888.

Sequence in context: A119971 A318290 A291986 * A094272 A236326 A308699

Adjacent sequences: A360886 A360887 A360888 * A360890 A360891 A360892

Keyword

nonn

Author

Seiichi Manyama, Feb 25 2023

Status

approved