A367693 G.f. A(x) satisfies A(x) = 1 / ((1 + x) * (1 - x * A(x^3))).

1, 0, 1, 0, 1, 0, 1, 1, 2, 2, 3, 3, 4, 5, 7, 9, 12, 15, 19, 24, 31, 40, 53, 68, 88, 113, 145, 186, 241, 311, 402, 519, 669, 861, 1110, 1431, 1846, 2382, 3073, 3962, 5109, 6586, 8492, 10952, 14125, 18216, 23493, 30294, 39063, 50373, 64959, 83769, 108030, 139314

Offset

0,9

Links

Table of n, a(n) for n=0..53.

Formula

a(n) = (-1)^n + Sum_{k=0..floor((n-1)/3)} a(k) * a(n-1-3*k).

Prog

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

Crossrefs

Cf. A005043, A351973, A367694.

Cf. A367659, A367691.

Sequence in context: A018243 A127207 A173513 * A147663 A301765 A374210

Adjacent sequences: A367690 A367691 A367692 * A367694 A367695 A367696

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2023

Status

approved