A019528 Poincaré series [or Poincare series] for depths of roots in a certain root system.

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

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 (0,1,2,2,0,-1,-2,-1,-1).

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: A111423 A153444 A175476 * A191695 A298915 A008945

Adjacent sequences: A019525 A019526 A019527 * A019529 A019530 A019531

Keyword

nonn,easy

Author

Robert G. Wilson v

Status

approved