A165879 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104376, 18691697667840, 299067162650760, 4785074601857280, 76561193620838400, 1224979097791365120, 19599665562389053440

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170736, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (15,15,15,15,15,15,15,15,15,-120).

Programs

GAP

a:=[17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104376];; for n in [11..30] do a[n]:=15*Sum([1..9], j-> a[n-j]) -120*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11) )); // G. C. Greubel, Sep 24 2019

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 24 2019

Mathematica

coxG[{10,120,-15}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 02 2015 *)
CoefficientList[Series[(1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11), {t, 0, 30}], t] (* G. C. Greubel, Sep 24 2019 *)

PARI

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11)) \\ G. C. Greubel, Sep 24 2019

Sage

def A165879_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11)).list()
A165879_list(30) # 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)/(120*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).