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

2,1

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).

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

Prog

(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

Crossrefs

Sequence in context: A181037 A222856 A342583 * A197050 A354387 A121188

Adjacent sequences: A007987 A007988 A007989 * A007991 A007992 A007993

Keyword

nonn,easy

Author

Stephen P. Humphries

Extensions

More terms from Ralf Stephan, Jun 11 2005

Status

approved