A390658 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - 2 * x * (1 + x + x^2 + x^3) * A(x^4))).

1, 3, 9, 27, 81, 247, 753, 2295, 6993, 21315, 64969, 198027, 603585, 1839735, 5607537, 17091847, 52096161, 158789763, 483993225, 1475217531, 4496481841, 13705334015, 41774032929, 127327785327, 388096714065, 1182923735699, 3605566637833, 10989813111003

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = 1 + 2 * Sum_{k=0..n-1} a(floor(k/4)) * a(n-1-k).

Mathematica

Clear[a]; a[0]=1; a[n_]:=a[n]=1+2*Sum[a[Floor[k/4]]*a[n-1-k], {k, 0, n-1}]; Table[a[n], {n, 0, 30}] (* Vincenzo Librandi, Jan 12 2026 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+2*sum(j=0, i-1, v[j\4+1]*v[i-j])); v;
(Magma) N := 40; a := [1]; for n in [1..N] do s := 1; for k in [0..n-1] do s +:= 2 * a[Floor(k/4) + 1] * a[n - k]; end for; Append(~a, s); end for; a; // Vincenzo Librandi, Jan 12 2026

Crossrefs

Cf. A162326, A390656, A390657.

Cf. A367715.

Sequence in context: A067500 A273898 A351343 * A078226 A083591 A052917

Adjacent sequences: A390655 A390656 A390657 * A390659 A390660 A390661

Keyword

nonn

Author

Seiichi Manyama, Nov 14 2025

Status

approved