A390660 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - 2 * x * A(x^3))).

1, 3, 7, 15, 37, 93, 229, 563, 1391, 3439, 8493, 20973, 51805, 127975, 316123, 780867, 1928877, 4764693, 11769661, 29073159, 71815939, 177398387, 438206105, 1082448217, 2673842665, 6604874695, 16315234267, 40301577123, 99552178897, 245911873753, 607446771249

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)/3)} a(k) * a(n-1-3*k).

Mathematica

a[0]=1; a[n_]:=a[n]=1+2*Sum[a[k]*a[n-1-3 k], {k, 0, Floor[(n-1)/3]}];
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)\3, v[j+1]*v[i-3*j])); v;
(Magma) a := [1]; for n in [1..30] do s := 0; for k in [0..Floor((n-1)/3)] do s +:= a[k+1] * a[n - 3*k]; end for; Append(~a, 1 + 2*s); end for; a; // Vincenzo Librandi, Jan 12 2026

Crossrefs

Cf. A162326, A390659, A390661.

Cf. A367691.

Sequence in context: A190571 A317881 A018020 * A192472 A147106 A078161

Adjacent sequences: A390657 A390658 A390659 * A390661 A390662 A390663

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 14 2025

Status

approved