A164071 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635069663, 97497551520, 3607408444536, 133474076864784, 4938539527424232, 182725913801503872, 6760857008268006426, 250151642617591466280, 9255608309383525500408

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170757, 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 (36, 36, 36, 36, 36, -666).

Programs

Mathematica

CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1), {t,0,50}], t] (* G. C. Greubel, Sep 09 2017 *)
coxG[{6,666,-36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 08 2023 *)

PARI

t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1)) \\ G. C. Greubel, Sep 09 2017

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).