A063809 - OEIS

%I #35 Jun 29 2023 17:38:21

%S 1,108,2160,40176,743040,13735872,253912320,4693641984,86763294720,

%T 1603843918848,29647506124800,548042492768256,10130719683870720,

%U 187269203879903232,3461723926449684480,63990940820356399104,1182890546466536816640

%N Spherical growth series for pair of groups, one Gromov hyperbolic, the other not.

%C Limit n -> infinity, a(n+1)/a(n) = 10+6*sqrt(2). - _Avi Friedlich_, Jun 02 2015

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

%H W. Floyd and W. Parry, <a href="http://dx.doi.org/10.1007/s002220050165">The growth of nonpositively curved triangles of groups</a>, Invent. math., 129 (1997), 289-359.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -28).

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

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

%F E.g.f.: 1 + 9*sqrt(2)*sinh(6*sqrt(2)*x)*exp(10*x). - _Ilya Gutkovskiy_, Jul 14 2016

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

%o (PARI) Vec((1+88*x+28*x^2)/(1-20*x+28*x^2) + O(x^30)) \\ _Michel Marcus_, Jun 02 2015

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Aug 20 2001