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A084203 G.f. A(x) defined by: A(x)^3 consists entirely of integer coefficients between 1 and 3 (A083953); A(x) is the unique power series solution with A(0)=1. 4
1, 1, 0, 0, 1, -1, 2, -2, 2, 0, -4, 12, -24, 38, -46, 33, 29, -176, 443, -827, 1222, -1310, 433, 2488, -8814, 19528, -33599, 44928, -37805, -17916, 168049, -463252, 921694, -1446018, 1679053, -808620, -2598482, 10515127, -24690122, 44515322, -62719429, 58496244, 10670109, -213311788, 632128236 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Does limit_{n ->infinity} a(n)/a(n+1) exist?

LINKS

Table of n, a(n) for n=0..44.

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 = 45;

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

coes = CoefficientList[A[x]^3 + O[x]^kmax , x];

r = {};

Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 3, a[k-1], Integers] // ToRules]; coes = coes /. r, {k, 1, kmax}];

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

CROSSREFS

Cf. A083953, A084202, A084204-A084212.

Sequence in context: A215461 A158851 A151930 * A073358 A124342 A082835

Adjacent sequences:  A084200 A084201 A084202 * A084204 A084205 A084206

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 19 2003

STATUS

approved

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Last modified June 18 17:05 EDT 2019. Contains 324214 sequences. (Running on oeis4.)