This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007990 PoincarĂ© series [or Poincare series] of Lie algebra associated with a certain braid group. 1

%I

%S 3,6,18,42,94,180,348,602,1047,1692,2737,4194,6426,9450,13863,19716,

%T 27933,38616,53160,71748,96396,127440,167704,217740,281439,359654,

%U 457617,576630,723592,900396,1116033,1373166,1683327,2050212,2488416,3002934,3612072

%N PoincarĂ© series [or Poincare series] of Lie algebra associated with a certain braid group.

%H Colin Barker, <a href="/A007990/b007990.txt">Table of n, a(n) for n = 2..1000</a>

%H S. P. Humphries, <a href="https://doi.org/10.1016/S0166-8641(98)00007-8">Braid groups, infinite Lie algebras of Cartan type and rings of invariants</a>, Topology and its Applications, 95 (3) (1999) pp. 173-205.

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-6,-5,4,10,4,-12,-8,0,8,12,-4,-10,-4,5,6,-3,-2,1).

%F 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

%F 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

%o (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

%K nonn,easy

%O 2,1

%A _Stephen P. Humphries_

%E More terms from _Ralf Stephan_, Jun 11 2005

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)