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%I #34 Feb 10 2020 01:36:34
%S 4,4,5,6,8,11,15,21,30,43,62,90,131,191,279,408,597,874,1280,1875,
%T 2747,4025,5898,8643,12666,18562,27203,39867,58427,85628,125493,
%U 183918,269544,395035,578951,848493,1243526,1822475,2670966,3914490,5736963,8407927
%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="/A019527/b019527.txt">Table of n, a(n) for n = 1..1000</a>
%H D. Pasechnik, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&threadID=561556&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#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1).
%F a(n) = 2*a(n-1)-a(n-2)+a(n-3)-a(n-4), for n>5.
%F G.f.: x*(x^4-4*x^3+x^2-4*x+4) / ((x-1)*(x^3+x-1)). - _Colin Barker_, Sep 27 2013
%F a(n) = a(n-1) + a(n-3) - 2, for n>4. - _Greg Dresden_, Feb 09 2020
%t CoefficientList[Series[(x^4 - 4 x^3 + x^2 - 4 x + 4)/((x - 1) (x^3 + x - 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 16 2013 *)
%t LinearRecurrence[{2,-1,1,-1},{4,4,5,6,8},50] (* _Harvey P. Dale_, Oct 11 2019 *)
%o (PARI) Vec(x*(x^4-4*x^3+x^2-4*x+4)/((x-1)*(x^3+x-1)) + O(x^100)) \\ _Colin Barker_, Sep 27 2013
%K nonn,easy
%O 1,1
%A _Robert G. Wilson v_
%E More terms from _Colin Barker_, Sep 27 2013
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