OFFSET
0,4
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.
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
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 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Aug 26 2002
STATUS
approved