A398041 G.f. A(x) satisfies A(x) = A(x^3) / (1-2*x), with A(0) = 1.

1, 2, 4, 10, 20, 40, 84, 168, 336, 682, 1364, 2728, 5476, 10952, 21904, 43848, 87696, 175392, 350868, 701736, 1403472, 2807112, 5614224, 11228448, 22457232, 44914464, 89828928, 179658538, 359317076, 718634152, 1437269668, 2874539336, 5749078672, 11498160072, 22996320144

Offset

0,2

Links

Table of n, a(n) for n=0..34.

Formula

G.f.: Product_{k>=0} 1/(1 - 2*x^(3^k)).

G.f.: 1 + 2 * Sum_{j>=0} x^(3^j) / Product_{k=0..j} (1 - 2*x^(3^k)).

a(0) = 1; for n >= 1, a(n) = 2*a(n-1) + a(n/3) if 3|n, and a(n) = 2*a(n-1) otherwise.

a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * a(k) for n >= 1.

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/prod(k=0, logint(N, 3), 1-2*x^3^k))

Crossrefs

Cf. A062051, A374626, A398042.

Sequence in context: A258092 A263993 A189585 * A239346 A004647 A265096

Adjacent sequences: A398036 A398039 A398040 * A398042 A398043 A398044

Keyword

nonn,new

Author

Seiichi Manyama, Jul 18 2026

Status

approved