A360890 G.f. satisfies A(x) = 1 + x/(1 - x^3) * A(x/(1 - x^3)).

1, 1, 1, 1, 2, 4, 7, 12, 25, 55, 115, 245, 564, 1331, 3103, 7407, 18388, 46198, 116503, 299966, 789426, 2095941, 5616114, 15299205, 42255533, 117689096, 331204936, 944052610, 2718150015, 7891518587, 23137661717, 68524545717, 204645635263, 616098009473

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-1-2*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-1-2*j, j)*v[i-3*j])); v;

Crossrefs

Cf. A000110, A172383, A360891.

Cf. A360898.

Sequence in context: A332338 A332836 A328129 * A309729 A027945 A079800

Adjacent sequences: A360887 A360888 A360889 * A360891 A360892 A360893

Keyword

nonn

Author

Seiichi Manyama, Feb 25 2023

Status

approved