A390659 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - 2 * x * A(x^2))).

1, 3, 7, 21, 61, 179, 527, 1561, 4617, 13667, 40455, 119765, 354541, 1049587, 3107183, 9198529, 27231329, 80615763, 238655191, 706515909, 2091572621, 6191900707, 18330529343, 54265778345, 160648643833, 475584938515, 1407923702391, 4168023401829, 12339034453917, 36528530817411

Offset

0,2

Links

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

Formula

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

Mathematica

a[0]=1; a[n_]:=a[n]=1+2*Sum[a[k]*a[n-1-2*k], {k, 0, Floor[(n-1)/2]}];
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)\2, v[j+1]*v[i-2*j])); v;
(Magma) a := [1]; for n in [1..30] do s := 0; for k in [0..Floor((n-1)/2)] do s +:= a[k+1] * a[n-2*k]; end for; Append(~a, 1 + 2*s); end for; a; // Vincenzo Librandi, Jan 12 2026

Crossrefs

Cf. A162326, A390660, A390661.

Cf. A351972.

Sequence in context: A345955 A091486 A056779 * A183113 A102877 A122983

Adjacent sequences: A390656 A390657 A390658 * A390660 A390661 A390662

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 14 2025

Status

approved