A166130 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469665841, 52073685498954240, 1718431621464879552, 56708243508320883072, 1871372035773924450624, 61755277180517572075776

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170753, 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 (32,32,32,32,32,32,32,32,32,-528).

Crossrefs

Cf. A154638, A170753.

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), {t,0,30}], t] (* G. C. Greubel, Apr 26 2016 *)
coxG[{528, 10, -32}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Sage

def A166130_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11) ).list()
A166130_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)/(528*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).