A019526 Poincaré series [or Poincare series] for depths of roots in a certain root system.

4, 5, 8, 13, 24, 44, 83, 158, 303, 582, 1120, 2157, 4156, 8009, 15436, 29752, 57347, 110538, 213067, 410698, 791644, 1525941, 2941344, 5669621, 10928544, 21065444, 40604947, 78268550, 150867479, 290806414, 560547384, 1080489821, 2082711092

Offset

1,1

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

D. Pasechnik, Poincare series for the depths of roots in a root system, Sci. Math. Research posting Oct 28 1996.

Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,-1).

Formula

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

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

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A101948 A348484 A087475 * A242014 A145488 A050892

Adjacent sequences: A019523 A019524 A019525 * A019527 A019528 A019529

Keyword

nonn,easy

Author

Robert G. Wilson v

Status

approved