A360885 G.f. satisfies A(x) = 1 + x * A(x * (1 + x^2)).

1, 1, 1, 1, 2, 4, 7, 16, 39, 93, 246, 671, 1884, 5578, 16887, 52854, 170649, 563703, 1914366, 6649798, 23610987, 85689987, 317054427, 1196183592, 4595744763, 17965311672, 71426213637, 288535755417, 1183807706841, 4929801601890, 20825803784129, 89210585925338

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..934

Formula

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

Crossrefs

Cf. A127782, A360886.

Cf. A360896.

Sequence in context: A260790 A151378 A192464 * A343869 A137568 A010355

Adjacent sequences: A360882 A360883 A360884 * A360886 A360887 A360888

Keyword

nonn

Author

Seiichi Manyama, Feb 25 2023

Status

approved