A073469 Expansion of x/B(x) where B(x) is the g.f. for A002487.

1, -1, -1, 2, -2, 0, 4, -4, -2, 6, -4, -2, 10, -8, -6, 14, -10, -4, 20, -16, -8, 24, -18, -6, 34, -28, -14, 42, -34, -8, 56, -48, -18, 66, -52, -14, 86, -72, -30, 102, -80, -22, 126, -104, -40, 144, -110, -34, 178, -144, -62, 206, -158, -48, 248, -200, -82, 282, -208, -74, 338, -264, -122, 386, -282, -104, 452, -348, -156, 504

Offset: 0

Author

N. J. A. Sloane, Aug 26 2002

Keywords

• sign

Comments

a(n) is the Euler transform of a sequence b(n) = [-1,-1,1,-1,0,1,0,-1,0,0,0,1 ...] that has (for n > 0, k > 0) b(2^k-1) = -1, b(3*2^k-1) = 1, and b(n) = 0 otherwise. - Georg Fischer, Aug 24 2020

Links

• Georg Fischer, Table of n, a(n) for n = 0..1000
• P. Dumas and P. Flajolet, Asymptotique des récurrences mahlériennes: le cas cyclotomique, Journal de Théorie des Nombres de Bordeaux 8 (1996), pp. 1-30.

Programs

Mathematica

terms = 70; A[x_] = 1/Product[1 + x^(2^k) + x^(2^(k + 1)), {k, 0, Ceiling[ Log[2, terms]]}] + O[x]^terms; CoefficientList[A[x], x] (* Jean-François Alcover, Jun 30 2011, updated Jan 15 2018 *)

Formula

This sequence grows asymptotically roughly like exp(log(n)^2), but with a complicated pattern of oscillations: see the article by Dumas-Flajolet, page 4, for a complete expansion that is related to A000123 and methods of de Bruijn. - Philippe Flajolet, Sep 06 2008

G.f. A(x) satisfies: A(x) = A(x^2) / (1 + x + x^2). - Ilya Gutkovskiy, Jul 09 2019