A166422 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698649794, 155653695863534232, 4202649788315149080, 113471544284501595192, 3063731695681342461048

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170747, 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 (26,26,26,26,26,26,26,26,26,26,-351).

Crossrefs

Cf. A154638, A169452, A170747.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-27*x+377*x^11-351*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

With[{p=351, q=26}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t,0,40}], t]] (* G. C. Greubel, May 13 2016; Jul 25 2024 *)
coxG[{11,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 22 2019 *)

SageMath

def A166422_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-27*x+377*x^11-351*x^12) ).list()
A166422_list(30) # G. C. Greubel, Jul 25 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)/(351*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

From G. C. Greubel, Jul 25 2024: (Start)

a(n) = 26*Sum_{j=1..10} a(n-j) - 351*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 27*x + 377*x^11 - 351*x^12). (End)