A166233 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505526393, 734448519232070580, 30846837807745372371, 1295567187925238776044, 54413821892857220325252

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), {t,0,30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10,861,-41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 10 2018 *)

Sage

def A166233_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11) ).list()
A166233_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)/(861*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).