A166167 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396730726, 135277862282282160, 4870003042161295290, 175320109517775581520, 6311523942638803173600

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170756, although the two sequences are eventually different.

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (35,35,35,35,35,35,35,35,35,-630).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11), {t,0,30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{630, 10, -35}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Sage

def A166167_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11) ).list()
A166167_list(30) # G. C. Greubel, Mar 11 2020

Formula

G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).