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A084206 G.f. A(x) defined by: A(x)^6 consists entirely of integer coefficients between 1 and 6 (A083946); A(x) is the unique power series solution with A(0)=1. 2
1, 1, -2, 7, -27, 115, -510, 2343, -11029, 52896, -257457, 1268098, -6307546, 31633044, -159757597, 811708539, -4145882814, 21273287952, -109603172373, 566748274099, -2940175511195, 15297961574259, -79808998488751, 417373462315834 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limit a(n)/a(n+1) -> r = -0.1815238859919 where A(r)=0.

LINKS

Table of n, a(n) for n=0..23.

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 = 25;

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

coes = CoefficientList[A[x]^6 + O[x]^(kmax + 1), x];

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

coes = coes /. r;

Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 6, 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. A083946, A084202-A084205, A084207-A084212.

Sequence in context: A150634 A150635 A150636 * A150637 A150638 A150639

Adjacent sequences:  A084203 A084204 A084205 * A084207 A084208 A084209

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 20 2003

STATUS

approved

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Last modified December 1 22:24 EST 2020. Contains 338858 sequences. (Running on oeis4.)