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Poincaré series [or Poincare series] for depths of roots in a certain root system.
1

%I #26 Jan 30 2018 18:57:35

%S 4,5,8,13,24,44,83,158,303,582,1120,2157,4156,8009,15436,29752,57347,

%T 110538,213067,410698,791644,1525941,2941344,5669621,10928544,

%U 21065444,40604947,78268550,150867479,290806414,560547384,1080489821,2082711092

%N Poincaré series [or Poincare series] for depths of roots in a certain root system.

%D Posting to sci.math.research by dima(AT)win.tue.nl (Dmitrii V. Pasechnik), Oct 28 1996.

%H Vincenzo Librandi, <a href="/A019526/b019526.txt">Table of n, a(n) for n = 1..1000</a>

%H D. Pasechnik, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=561556&amp;messageID=1681290#1681290">Poincare series for the depths of roots in a root system</a>, Sci. Math. Research posting Oct 28 1996.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,-1).

%F a(n) = 2a(n-1)-a(n-5).

%F G.f.: -x*(2*x^4+3*x^3+2*x^2+3*x-4) / ((x-1)*(x^4+x^3+x^2+x-1)). - _Colin Barker_, Sep 27 2013

%t CoefficientList[Series[-(2 x^4 + 3 x^3 + 2 x^2 + 3 x - 4)/((x - 1) (x^4 + x^3 + x^2 + x - 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 27 2013 *)

%o (PARI) Vec(-x*(2*x^4+3*x^3+2*x^2+3*x-4)/((x-1)*(x^4+x^3+x^2+x-1)) + O(x^100)) \\ _Colin Barker_, Sep 27 2013

%K nonn,easy

%O 1,1

%A _Robert G. Wilson v_