A163969 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 20, 380, 7220, 137180, 2606420, 49521790, 940910400, 17877229200, 339666055200, 6453630356400, 122618507616000, 2329742730783510, 44264942521047180, 841030689999256020, 15979521970107624780

Offset: 0

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170739, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, -171).

Programs

Mathematica

coxG[{6,171,-18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 21 2015 *)
CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 23 2017 *)

PARI

t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)) \\ G. C. Greubel, Aug 23 2017

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).