A166230 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244545501, 563751691026330240, 23113819332078093360, 947666592615142522080, 38854330297218411872400

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170761, 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 (40, 40, 40, 40, 40, 40, 40, 40, 40, -820).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), {t,0,30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10, 820, -40}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Sage

def A166230_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11) ).list()
A166230_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)/(820*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).