A398040 G.f. A(x) satisfies A(x) = A(x^2) / (1-4*x), with A(0) = 1.

1, 4, 20, 80, 340, 1360, 5520, 22080, 88660, 354640, 1419920, 5679680, 22724240, 90896960, 363609920, 1454439680, 5817847380, 23271389520, 93085912720, 372343650880, 1489376023440, 5957504093760, 23830022054720, 95320088218880, 381280375599760, 1525121502399040

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: Product_{k>=0} 1/(1 - 4*x^(2^k)).

G.f.: 1 + 4 * Sum_{j>=0} x^(2^j) / Product_{k=0..j} (1 - 4*x^(2^k)).

a(0) = 1; for n >= 1, a(n) = 4*a(n-1) + a(n/2) if 2|n, and a(n) = 4*a(n-1) otherwise.

a(n) = Sum_{k=0..floor(n/2)} 4^(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), 1-4*x^2^k))

Crossrefs

Cf. A018819, A309728, A398039.

Sequence in context: A371408 A292540 A320934 * A344063 A055296 A140532

Adjacent sequences: A398031 A398036 A398039 * A398041 A398042 A398043

Keyword

nonn,new

Author

Seiichi Manyama, Jul 18 2026

Status

approved