A309728 G.f. A(x) satisfies: A(x) = A(x^2) / (1 - 2*x).

1, 2, 6, 12, 30, 60, 132, 264, 558, 1116, 2292, 4584, 9300, 18600, 37464, 74928, 150414, 300828, 602772, 1205544, 2413380, 4826760, 9658104, 19316208, 38641716, 77283432, 154585464, 309170928, 618379320, 1236758640, 2473592208, 4947184416, 9894519246, 19789038492, 39578377812

Offset

0,2

Links

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

Formula

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

Mathematica

nmax = 34; A[_] = 1; Do[A[x_] = A[x^2]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 34; CoefficientList[Series[Product[1/(1 - 2 x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Prog

(PARI) seq(n)=Vec(1/prod(k=0, logint(n, 2), 1 - 2*x^(2^k) + O(x*x^n))) \\ Andrew Howroyd, Aug 14 2019

Crossrefs

Cf. A001316, A018819, A171238, A308986.

Sequence in context: A330542 A166456 A162214 * A100071 A331552 A129912

Adjacent sequences: A309725 A309726 A309727 * A309729 A309730 A309731

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 14 2019

Status

approved