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A084205 G.f. A(x) defined by: A(x)^5 consists entirely of integer coefficients between 1 and 5 (A083945); A(x) is the unique power series solution with A(0)=1. 3
1, 1, -1, 3, -8, 24, -76, 252, -854, 2950, -10343, 36706, -131570, 475576, -1731357, 6342042, -23356185, 86421603, -321111661, 1197586539, -4481348585, 16819759474, -63302097780, 238835017492, -903165412289, 3422512973645, -12994514592311, 49425252955926 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Limit a(n)/a(n+1) -> r = -0.2512525316047635 where A(r)=0.

LINKS

Table of n, a(n) for n=0..27.

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]^5 + O[x]^(kmax + 1), x];

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

coes = coes /. r;

Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 5, a[k-1], Integers] // ToRules];

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

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

CROSSREFS

Cf. A083945, A084202-A084204, A084206-A084212.

Sequence in context: A000958 A148782 A148783 * A118099 A066350 A148784

Adjacent sequences:  A084202 A084203 A084204 * A084206 A084207 A084208

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 20 2003

STATUS

approved

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Last modified December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)