A019527 Poincaré series [or Poincare series] for depths of roots in a certain root system.

4, 4, 5, 6, 8, 11, 15, 21, 30, 43, 62, 90, 131, 191, 279, 408, 597, 874, 1280, 1875, 2747, 4025, 5898, 8643, 12666, 18562, 27203, 39867, 58427, 85628, 125493, 183918, 269544, 395035, 578951, 848493, 1243526, 1822475, 2670966, 3914490, 5736963, 8407927

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,-1,1,-1).

Formula

a(n) = 2*a(n-1)-a(n-2)+a(n-3)-a(n-4), for n>5.

G.f.: x*(x^4-4*x^3+x^2-4*x+4) / ((x-1)*(x^3+x-1)). - Colin Barker, Sep 27 2013

a(n) = a(n-1) + a(n-3) - 2, for n>4. - Greg Dresden, Feb 09 2020

Mathematica

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 *)
LinearRecurrence[{2, -1, 1, -1}, {4, 4, 5, 6, 8}, 50] (* Harvey P. Dale, Oct 11 2019 *)

Prog

(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

Crossrefs

Sequence in context: A243427 A085581 A137902 * A062836 A137903 A091349

Adjacent sequences: A019524 A019525 A019526 * A019528 A019529 A019530

Keyword

nonn,easy

Author

Robert G. Wilson v

Extensions

More terms from Colin Barker, Sep 27 2013

Status

approved