A367692 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - x * A(x^4))).

1, 2, 3, 4, 5, 8, 13, 20, 29, 43, 66, 102, 155, 233, 352, 536, 817, 1240, 1878, 2848, 4327, 6576, 9984, 15150, 22995, 34919, 53029, 80513, 122224, 185556, 281736, 427776, 649481, 986054, 1497069, 2272976, 3451038, 5239607, 7955067, 12077876, 18337503

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)/4)} a(k) * a(n-1-4*k).

Mathematica

Clear[a]; a[0]=1; a[n_]:=a[n]=1+Sum[a[k] a[n-1-4 k], {k, 0, Floor[(n-1)/4]}]; 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)\4, v[j+1]*v[i-4*j])); v;
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A367692(n): return 1+sum(A367692(k)*A367692(n-1-(k<<2)) for k in range(n+3>>2)) # Chai Wah Wu, Nov 30 2023
(Magma) N := 40; a := [1]; for n in [1..N-1] do s := 1; for k in [0..Floor((n-1)/4)] do s := s + a[k+1] * a[n - 4*k]; end for; Append(~a, s); end for; a; // Vincenzo Librandi, Jan 11 2026

Crossrefs

Cf. A007317, A351972, A367691.

Cf. A367660.

Sequence in context: A249581 A051706 A292325 * A307971 A346073 A211696

Adjacent sequences: A367689 A367690 A367691 * A367693 A367694 A367695

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2023

Status

approved