A390657 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - 2 * x * (1 + x + x^2) * A(x^3))).

1, 3, 9, 27, 85, 267, 837, 2631, 8269, 25983, 81657, 256623, 806473, 2534483, 7965057, 25031547, 78665957, 247221355, 776935701, 2441654415, 7673320077, 24114731415, 75784701705, 238166493207, 748479273097, 2352225180067, 7392273235777, 23231493333387

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

Mathematica

Clear[a]; a[0]=1; a[n_]:=a[n]=1+2*Sum[a[Floor[k/3]]*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\3+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/3) + 1] * a[n - k]; end for; Append(~a, s); end for; a; // Vincenzo Librandi, Jan 11 2026

Crossrefs

Cf. A162326, A390656, A390658.

Cf. A367714.

Sequence in context: A099787 A351342 A308520 * A176826 A146786 A151029

Adjacent sequences: A390654 A390655 A390656 * A390658 A390659 A390660

Keyword

nonn

Author

Seiichi Manyama, Nov 14 2025

Status

approved