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%I #27 Aug 13 2020 22:17:19
%S 1,4,9,16,26,41,62,90,128,181,254,352,483,660,900,1224,1661,2252,3052,
%T 4133,5592,7562,10224,13821,18680,25244,34113,46096,62284,84152,
%U 113695,153608,207530,280377,378792,511750,691374,934041,1261878,1704780,2303133,3111496,4203578,5678960,7672173,10364964
%N Poincaré series for hyperbolic reflection group with Coxeter diagram o---o-(5)-o---o.
%C The diagram is o---o-(5)-o---o.
%H Colin Barker, <a href="/A265044/b265044.txt">Table of n, a(n) for n = 0..1000</a>
%H Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, <a href="http://arxiv.org/abs/0906.1596">The Poincaré series of the hyperbolic Coxeter groups with finite volume of fundamental domains</a>, arXiv:0906.1596 [math.RT], 2009.
%H Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, <a href="http://dx.doi.org/10.1142/S1402925110000842">The Poincaré series of the hyperbolic Coxeter groups with finite volume of fundamental domains</a>, Journal of Nonlinear Mathematical Physics 17.supp01 (2010): 169-215.
%H R. L. Worthington, <a href="http://dx.doi.org/10.4153/CMB-1998-033-5">The growth series of compact hyperbolic Coxeter groups, with 4 and 5 generators</a>, Canad. Math. Bull. 41(2) (1998) 231-239.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,2,-1,0,1,-2,1).
%F G.f.: -b(2)*b(3)*(1+x^3)*(1+x^5)/((x-1)*(x^10-x^9-x^6+x^5-x^4-x+1)) where b(k) = (1-x^k)/(1-x).
%F G.f.: (1+x)^3*(1-x+x^2)*(1+x+x^2)*(1-x+x^2-x^3+x^4) / ((1-x)*(1-x-x^4+x^5-x^6-x^9+x^10)). - _Colin Barker_, Jan 01 2016
%o (PARI) Vec((1+x)^3*(1-x+x^2)*(1+x+x^2)*(1-x+x^2-x^3+x^4)/((1-x)*(1-x-x^4+x^5-x^6-x^9+x^10)) + O(x^50)) \\ _Colin Barker_, Jan 01 2016
%Y Poincaré series in this family: A265044 and A265047 - A265054.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 27 2015
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