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A084208 G.f. A(x) defined by: A(x)^8 consists entirely of integer coefficients between 1 and 8 (A083948); A(x) is the unique power series solution with A(0)=1. 2
1, 1, -3, 15, -82, 484, -2992, 19110, -124979, 832234, -5621028, 38402783, -264858143, 1841221687, -12886279885, 90713376563, -641815393278, 4561172770669, -32542369727538, 232992967457839 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limit a(n)/a(n+1) --> r = -0.131401689761435 where A(r)=0.

LINKS

Table of n, a(n) for n=0..19.

MATHEMATICA

kmax = 20;

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

coes = CoefficientList[A[x]^8 + O[x]^(kmax + 1), x];

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

coes = coes /. r;

Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 8, 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. A083948, A084202-A084207, A084209-A084212.

Sequence in context: A264225 A255676 A015680 * A059271 A014276 A006964

Adjacent sequences:  A084205 A084206 A084207 * A084209 A084210 A084211

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 20 2003

STATUS

approved

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Last modified December 3 18:22 EST 2020. Contains 338910 sequences. (Running on oeis4.)