A166128 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909140976, 26228105183354880, 813071260683525120, 25205209081174517760, 781361481515952460800, 24222205926980341002240

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170751, 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 (30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*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 -31*t +495*t^10 -465*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)
coxG[{465, 10, -30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Sage

def A166128_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11) ).list() A166128_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)/(465*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).