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.

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

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-François Alcover, Jul 26 2018 *)

Crossrefs

Cf. A083953, A084202, A084204-A084212.

Sequence in context: A158851 A151930 A356907 * A073358 A124342 A324244

Adjacent sequences: A084200 A084201 A084202 * A084204 A084205 A084206

Keyword

sign

Author

Paul D. Hanna, May 19 2003

Status

approved