A166382 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824535, 60743477542020, 850408685567805, 11905721597662620, 166680102363263580, 2333521433029506720

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 (13,13,13,13,13,13,13,13,13,13,-91).

Crossrefs

Cf. A154638, A169452, A170734.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-14*x+104*x^11-91*x^12) )); // G. C. Greubel, Jul 23 2024

Mathematica

With[{a=91, b=13}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(b+1)*t +(a+b)*t^11-a*t^12), {t,0,40}], t]] (* G. C. Greubel, May 10 2016; Jul 23 2024 *)
coxG[{11,91,-13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 25 2019 *)

SageMath

def A166382_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-14*x+104*x^11-91*x^12) ).list()
A166382_list(30) # G. C. Greubel, Jul 23 2024

Formula

G.f.: (t^11 + 2*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^11 - 13*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).

From G. C. Greubel, Jul 23 2024: (Start)

a(n) = 13*Sum_{j=1..10} a(n-j) - 91*a(n-11).

G.f.: (1+x)*(1 - x^11)/(1 - 14*x + 104*x^11 - 91*x^12). (End)