A165875 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701655, 4338819821700, 60743477483325, 850408684479900, 11905721578705500, 166680102045693600, 2333521427853142800

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170734, 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 (13,13,13,13,13,13,13,13,13,-91).

Programs

GAP

a:=[15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701655];; for n in [11..20] do a[n]:=13*Sum([1..9], j-> a[n-j]) -19*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 23 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11) )); // G. C. Greubel, Sep 23 2019

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 23 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 91, -13}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 23 2019 *)

PARI

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11)) \\ G. C. Greubel, Sep 23 2019

Sage

def A165875_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11)).list()
A165875_list(30) # G. C. Greubel, Sep 23 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)/(91*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).