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A063809 Spherical growth series for pair of groups, one Gromov hyperbolic, the other not. 0
1, 108, 2160, 40176, 743040, 13735872, 253912320, 4693641984, 86763294720, 1603843918848, 29647506124800, 548042492768256, 10130719683870720, 187269203879903232, 3461723926449684480, 63990940820356399104, 1182890546466536816640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Limit n -> infinity, a(n+1)/a(n) = 10+6*sqrt(2). - Avi Friedlich, Jun 02 2015

REFERENCES

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 154.

LINKS

Table of n, a(n) for n=0..16.

W. Floyd and W. Parry, The growth of nonpositively curved triangles of groups, Invent. math., 129 (1997), 289-359.

FORMULA

G.f.: (1+88*x+28*x^2)/(1-20*x+28*x^2).

a(n) = 9*((10+6*sqrt(2))^n-(10-6*sqrt(2))^n)/sqrt(2), n>0. - Benedict W. J. Irwin, Jul 14 2016

E.g.f.: 1 + 9*sqrt(2)*sinh(6*sqrt(2)*x)*exp(10*x). - Ilya Gutkovskiy, Jul 14 2016

MATHEMATICA

CoefficientList[Series[(1 + 88 x + 28 x^2)/(1 - 20 x + 28 x^2), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 02 2015 *)

PROG

(PARI) Vec((1+88*x+28*x^2)/(1-20*x+28*x^2) + O(x^30)) \\ Michel Marcus, Jun 02 2015

CROSSREFS

Sequence in context: A250339 A263961 A202427 * A183357 A264681 A221018

Adjacent sequences:  A063806 A063807 A063808 * A063810 A063811 A063812

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 20 2001

STATUS

approved

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Last modified May 26 12:47 EDT 2022. Contains 354091 sequences. (Running on oeis4.)