A165967 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505300, 1585084524120000, 38042028578707500, 913008685884840000, 21912208461136800000, 525893003064898560000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170744, 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 (23,23,23,23,23,23,23,23,23,-276).

Programs

GAP

a:=[25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505300];; for n in [11..30] do a[n]:=23*Sum([1..9], j-> a[n-j]) -276*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 26 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11) )); // G. C. Greubel, Sep 26 2019

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 26 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 18 2016 *)
coxG[{10, 276, -23}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 26 2019 *)

PARI

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11)) \\ G. C. Greubel, Sep 26 2019

Sage

def A165967_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11)).list()
A165967_list(30) # G. C. Greubel, Sep 26 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)/(276*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).