A390656 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - 2 * x * (1 + x) * A(x^2))).

1, 3, 9, 31, 105, 363, 1249, 4319, 14913, 51539, 178057, 615279, 2125929, 7345883, 25382305, 87704607, 303048289, 1047133859, 3618196393, 12502080287, 43198864521, 149266526667, 515765751745, 1782143145119, 6157900445473, 21277605119731, 73521240305833

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/2)) * a(n-1-k).

Mathematica

Clear[a]; a[0]=1; a[n_]:=a[n]=1+2*Sum[a[Floor[k/2]]*a[n-1-k], {k, 0, n-1}]; 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+2*sum(j=0, i-1, v[j\2+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/2) + 1] * a[n - k]; end for; Append(~a, s); end for; a; // Vincenzo Librandi, Jan 11 2026

Crossrefs

Cf. A162326, A390657, A390658.

Cf. A367713.

Sequence in context: A027096 A221440 A289599 * A148964 A148965 A130620

Adjacent sequences: A390653 A390654 A390655 * A390657 A390658 A390659

Keyword

nonn

Author

Seiichi Manyama, Nov 14 2025

Status

approved