A166026 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379275635, 12621216998980800, 366015292970077800, 10614443496121659600, 307818861387220827000, 8926746980220492242400

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170749, 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 (28,28,28,28,28,28,28,28,28,-406).

Programs

GAP

a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379275635];; for n in [11..30] do a[n]:=28*Sum([1..9], j-> a[n-j]) - 406*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Dec 05 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11) )); // G. C. Greubel, Dec 05 2019

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Dec 05 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), {t,0,30}], t] (* G. C. Greubel, Apr 21 2016 *)
coxG[{10,406,-28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 13 2020 *)

PARI

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)) \\ G. C. Greubel, Dec 05 2019

Sage

def A166026_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)).list()
A166026_list(30) # G. C. Greubel, Dec 05 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)/(406*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).