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A019527 Poincaré series [or Poincare series] for depths of roots in a certain root system. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 28 05:40 EDT 2022. Contains 354903 sequences. (Running on oeis4.)