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A019528
Poincaré series [or Poincare series] for depths of roots in a certain root system.
1
5, 5, 6, 8, 11, 16, 25, 38, 59, 93, 148, 235, 376, 602, 966, 1550, 2491, 4003, 6436, 10348, 16643, 26766, 43052, 69247, 111387, 179169, 288207, 463601, 745744, 1199593, 1929661, 3104041, 4993156, 8031978, 12920238, 20783483, 33432314, 53779215
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+1) = sum_{i=n-11}^n v(i)*a(i), where v = [ 0,0,-1,-1,-2,-1,0,2,2,1,0 ].
G.f.: x*(x^10+3*x^9+x^8-x^7-9*x^6-14*x^5-15*x^4-7*x^3+x^2+5*x+5) / (x^9+x^8+2*x^7+x^6-2*x^4-2*x^3-x^2+1). [Colin Barker, Nov 28 2012]
MATHEMATICA
CoefficientList[Series[(x^10 + 3 x^9 + x^8 - x^7 - 9 x^6 - 14 x^5 - 15 x^4 - 7 x^3 + x^2 + 5 x + 5)/ (x^9 + x^8 + 2 x^7 + x^6 - 2 x^4 - 2 x^3 - x^2 + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 16 2013 *)
CROSSREFS
Sequence in context: A153444 A175476 A376743 * A191695 A298915 A008945
KEYWORD
nonn,easy
STATUS
approved