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A073469 G.f.: x/B(x) where B(x) = g.f. for A002487. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..69.

P. Dumas and P. Flajolet, Asymptotique des recurrences mahleriennes: le cas cyclotomique, Journal de Theorie des Nombres de Bordeaux 8 (1996), pp. 1-30.

FORMULA

Comment from Philippe Flajolet, Sep 06 2008: 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.

MATHEMATICA

m = 69; f[x_] = Sum[c[k] x^k, {k, 0, m}]; c[0] = 1; c[1] = -1; c[2] = -1;

eq[3] = Thread[ CoefficientList[f[x]^2*f[x^4] + 2*x*f[x]*f[x^2]^2 - f[x^2]^3, x] == 0][[4 ;; ]];

Do[s[k] = Solve[eq[k] // First, c[k]] // First; eq[k + 1] = eq[k] /. s[k] // Rest, {k, 3, m}];

Table[c[k], {k, 0, m}] /. Flatten[Table[s[k], {k, 3, m}]]

(* Jean-Fran├žois Alcover, Jun 30 2011, after g.f. *)

CROSSREFS

Sequence in context: A078029 A078030 A241320 * A086882 A168587 A100240

Adjacent sequences:  A073466 A073467 A073468 * A073470 A073471 A073472

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Aug 26 2002

STATUS

approved

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Last modified September 2 22:02 EDT 2014. Contains 246369 sequences.