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A084207 G.f. A(x) defined by: A(x)^7 consists entirely of integer coefficients between 1 and 7 (A083947); A(x) is the unique power series solution with A(0)=1. 3
1, 1, -2, 8, -34, 158, -768, 3858, -19851, 104023, -552974, 2973832, -16146688, 88376636, -487034106, 2699839758, -15043262970, 84197804254, -473140314356, 2668221663736, -15095165871964, 85645090974518, -487190919969502 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limit a(n)/a(n+1) -> r = -0.166670835025545 where A(r)=0.

LINKS

Table of n, a(n) for n=0..22.

MATHEMATICA

kmax = 25;

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

coes = CoefficientList[A[x]^7 + O[x]^(kmax + 1), x];

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

coes = coes /. r;

Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 7, 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. A083947, A084202-A084206, A084208-A084212.

Sequence in context: A150898 A150899 A150900 * A151305 A150901 A046649

Adjacent sequences:  A084204 A084205 A084206 * A084208 A084209 A084210

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 20 2003

STATUS

approved

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Last modified June 26 23:07 EDT 2022. Contains 354885 sequences. (Running on oeis4.)