A166313 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708931688, 2524758347319736320, 118663642324025116416, 5577191189229063412224, 262127985893760478586112

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170767, 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 (46,46,46,46,46,46,46,46,46,-1081).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11), {t,0,30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10,1081,-46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 05 2017 *)

Sage

def A166313_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11) ).list()
A166313_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)/(1081*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).