A166325 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895521225, 3989613314880480000, 195491052429140580000, 9579061569027744360000, 469374016882352414700000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170769, 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 (48,48,48,48,48,48,48,48,48,-1176).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 12 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), {t,0,30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10, 1176, -48}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)

Sage

def A166325_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11) ).list()
A166325_list(30) # G. C. Greubel, Aug 10 2019

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)/(1176*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).