A367691 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - x * A(x^3))).

1, 2, 3, 4, 7, 12, 19, 31, 52, 86, 141, 233, 386, 639, 1057, 1749, 2896, 4795, 7937, 13138, 21751, 36010, 59613, 98688, 163380, 270479, 447779, 741300, 1227231, 2031697, 3363494, 5568295, 9218373, 15261119, 25264942, 41826373, 69244006, 114634194, 189778123

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Formula

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

Mathematica

Clear[a]; a[0]=1; a[n_]:=a[n]=1+Sum[a[k] a[n-1-3* k], {k, 0, Floor[(n-1)/3]}]; Table[a[n], {n, 0, 40}] (* Vincenzo Librandi, Jan 11 2026 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, (i-1)\3, v[j+1]*v[i-3*j])); v;
(Magma) N := 40; a := [1]; for n in [1..N-1] do s := 1; for k in [0..Floor((n-1)/3)] do s := s + a[k+1] * a[n - 3*k]; end for; Append(~a, s); end for; a; // Vincenzo Librandi, Jan 11 2026

Crossrefs

Cf. A007317, A351972, A367692.

Cf. A367659.

Sequence in context: A293411 A227047 A298304 * A307970 A216604 A211695

Adjacent sequences: A367688 A367689 A367690 * A367692 A367693 A367694

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2023

Status

approved