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A084204 G.f. A(x) defined by: A(x)^4 consists entirely of integer coefficients between 1 and 4 (A083954); A(x) is the unique power series solution with A(0)=1. 2
1, 1, -1, 3, -7, 20, -58, 177, -554, 1769, -5739, 18866, -62684, 210146, -709882, 2413743, -8253995, 28366316, -97916761, 339326189, -1180068800, 4116957243, -14404398636, 50530280752, -177684095927, 626181400993, -2211215950469, 7823025701314, -27724997048327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Limit a(n)/a(n+1) -> r = -0.269562488839799 where A(r)=0.

LINKS

Table of n, a(n) for n=0..28.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

MATHEMATICA

kmax = 30;

A[x_] = Sum[a[k] x^k, {k, 0, kmax}];

coes = CoefficientList[A[x]^4 + O[x]^(kmax + 1), x];

r = {a[0] -> 1, a[1] -> 1}; coes = coes /. r;

Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 4, a[k-1], Integers] // ToRules];

coes = coes /. r, {k, 3, kmax + 1}];

Table[a[k], {k, 0, kmax}] /. r (* Jean-Fran├žois Alcover, Jul 26 2018 *)

CROSSREFS

Cf. A083954, A084202, A084203, A084205-A084212.

Sequence in context: A274478 A238124 A129429 * A030238 A132364 A110490

Adjacent sequences:  A084201 A084202 A084203 * A084205 A084206 A084207

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 20 2003

STATUS

approved

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Last modified June 25 05:41 EDT 2019. Contains 324346 sequences. (Running on oeis4.)