A398039 G.f. A(x) satisfies A(x) = A(x^2) / (1-3*x), with A(0) = 1.

1, 3, 12, 36, 120, 360, 1116, 3348, 10164, 30492, 91836, 275508, 827640, 2482920, 7452108, 22356324, 67079136, 201237408, 603742716, 1811228148, 5433776280, 16301328840, 48904262028, 146712786084, 440139185892, 1320417557676, 3961255155948, 11883765467844, 35651303855640

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

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

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

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/prod(k=0, logint(N, 2), 1-3*x^2^k))

Crossrefs

Cf. A018819, A309728, A398040.

Sequence in context: A027327 A290927 A167993 * A061130 A247008 A344062

Adjacent sequences: A398027 A398028 A398036 * A398040 A398041 A398042

Keyword

nonn,new

Author

Seiichi Manyama, Jul 18 2026

Status

approved