A164548 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314365, 47828880, 430456320, 3874074480, 34866378720, 313794784080, 2824129437120, 25416952359660, 228750658083360, 2058738704511840, 18528493377756960, 166755045745830240

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003952, 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..1000
• Index entries for linear recurrences with constant coefficients, signature (8,8,8,8,8,8,-36).

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) )); // G. C. Greubel, Jul 17 2021

Mathematica

CoefficientList[Series[(1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8), {t,0,30}], t] (* or *)
coxG[{7, 36, -8, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 17 2021 *)

Sage

def A168823_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) ).list()
A168823_list(30) # G. C. Greubel, Jul 17 2021

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

G.f.: (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8). - G. C. Greubel, Jul 17 2021