A165882 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955390, 122621325148800, 2329805177758800, 44266298376117600, 841059669121542000, 15980133712840142400

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170739, 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 (18,18,18,18,18,18,18,18,18,-171).

Crossrefs

Cf. A154638, A170739.

Programs

GAP

a:=[20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955390];; for n in [11..20] do a[n]:=18*Sum([1..9], j-> a[n-j]) -171*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11) )); // G. C. Greubel, Sep 24 2019

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 24 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10,171,-18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 18 2018 *)

PARI

my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11)) \\ G. C. Greubel, Sep 24 2019

Sage

def A165882_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11)).list()
A165882_list(20) # G. C. Greubel, Sep 24 2019

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)/(171*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).