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A019525 Poincaré series [or Poincare series] for depths of roots in a certain root system. 1
2, 3, 6, 12, 27, 60, 138, 315, 726, 1668, 3843, 8844, 20370, 46899, 108006, 248700, 572715, 1318812, 3036954, 6993387, 16104246, 37084404, 85397139, 196650348, 452841762, 1042792803, 2401318086, 5529696492, 12733650747, 29322740220 (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
D. Pasechnik, Poincare series for the depths of roots in a root system, Sci. Math. Research posting Oct 28 1996.
FORMULA
a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3).
G.f.: -x*(4*x^2+x-2) / ((x-1)*(3*x^2+x-1)). - Colin Barker, Sep 27 2013
a(n) = (78 + (13-5*sqrt(13))*((1-sqrt(13))/2)^n + ((1+sqrt(13))/2)^n*(13+5*sqrt(13))) / 78. - Colin Barker, Aug 03 2017
MATHEMATICA
CoefficientList[Series[-(4 x^2 + x - 2)/((x - 1) (3 x^2 + x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 27 2013 *)
LinearRecurrence[{2, 2, -3}, {2, 3, 6}, 30] (* Harvey P. Dale, Nov 28 2014 *)
PROG
(PARI) Vec(-x*(4*x^2+x-2)/((x-1)*(3*x^2+x-1)) + O(x^100)) \\ Colin Barker, Sep 27 2013
CROSSREFS
Sequence in context: A339150 A024422 A186771 * A108915 A082395 A061343
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 03:21 EDT 2024. Contains 370952 sequences. (Running on oeis4.)