A166170 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212223, 182726206151826240, 6760869627616609176, 250152176221778956464, 9255630520204504816392

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170757, 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 (36,36,36,36,36,36,36,36,36,-666).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-37*t+702*t^10-666*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-37*t+702*t^10-666*t^11), {t,0,30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{666, 10, -36}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Sage

def A166170_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-37*t+702*t^10-666*t^11) ).list()
A166170_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)/(666*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).