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A019526
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Poincaré series [or Poincare series] for depths of roots in a certain root system.
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1
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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
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OFFSET
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1,1
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REFERENCES
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Posting to sci.math.research by dima(AT)win.tue.nl (Dmitrii V. Pasechnik), Oct 28 1996.
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A101948 A348484 A087475 * A242014 A145488 A050892
Adjacent sequences: A019523 A019524 A019525 * A019527 A019528 A019529
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KEYWORD
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nonn,easy
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AUTHOR
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Robert G. Wilson v
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STATUS
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approved
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