A007990 Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group.
3, 6, 18, 42, 94, 180, 348, 602, 1047, 1692, 2737, 4194, 6426, 9450, 13863, 19716, 27933, 38616, 53160, 71748, 96396, 127440, 167704, 217740, 281439, 359654, 457617, 576630, 723592, 900396, 1116033, 1373166, 1683327, 2050212, 2488416, 3002934, 3612072
Offset: 2
Links
- Colin Barker, Table of n, a(n) for n = 2..1000
- S. P. Humphries, Braid groups, infinite Lie algebras of Cartan type and rings of invariants, Topology and its Applications, 95 (3) (1999) pp. 173-205.
- Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-5,4,10,4,-12,-8,0,8,12,-4,-10,-4,5,6,-3,-2,1).
Programs
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PARI
Vec(x^2*(3 - 3*x^2 + 6*x^3 + 7*x^4 - 8*x^5 - 6*x^6 - 4*x^7 + 13*x^8 + 8*x^9 - 8*x^11 - 14*x^12 + 6*x^13 + 6*x^14 + 6*x^15 - 3*x^16 - 6*x^17 + 3*x^18) / ((1 - x)^9*(1 + x)^5*(1 + x^2)*(1 + x + x^2)^2) + O(x^50)) \\ Colin Barker, Aug 03 2017
Formula
The Humphries paper gives a g.f. with denominator (1-x^4)*(1-x^3)^2*(1-x^2)^4*(1-x)^2. - Ralf Stephan, Jun 11 2005
G.f.: x^2*(3 - 3*x^2 + 6*x^3 + 7*x^4 - 8*x^5 - 6*x^6 - 4*x^7 + 13*x^8 + 8*x^9 - 8*x^11 - 14*x^12 + 6*x^13 + 6*x^14 + 6*x^15 - 3*x^16 - 6*x^17 + 3*x^18) / ((1 - x)^9*(1 + x)^5*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Aug 02 2017
Extensions
More terms from Ralf Stephan, Jun 11 2005