A166368 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867843965, 313810595280, 2824295353920, 25418658152880, 228767923084320, 2058911305134480, 18530201722590720, 166771815290740080

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,8,8,8,8,8,-36).

Crossrefs

Cf. A003952, A154638, A169452.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-9*x+44*x^16-36*x^17) )); // G. C. Greubel, Jul 23 2024

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 14 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), {t,0,30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 36, -8}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 14 2020 *)

Sage

def A166368_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12) ).list()
A166368_list(30) # G. C. Greubel, Mar 14 2020

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)/(36*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

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

a(n) = 8*Sum_{j=1..10} a(n-j) - 36*a(n-11).

G.f.: (1+t)*(1 - t^11)/(1 - 9*t + 44*t^11 - 36*t^12). (End)