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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 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.)