A166418 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127300, 22867434189921552, 525950986368049968, 12096872686461797520, 278228071788544252848

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170743, 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 (22,22,22,22,22,22,22,22,22,22,-253).

Crossrefs

Cf. A154638, A169452, A170743.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-23*x+275*x^11-253*x^12) )); // G. C. Greubel, Jul 23 2024

Mathematica

With[{p=253, q=22}, 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 23 2024 *)
coxG[{11, 253, -22, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 23 2024 *)

SageMath

def A166418_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-23*x+275*x^11-253*x^12) ).list()
A166418_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)/(253*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

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

a(n) = 22*Sum_{j=1..10} a(n-j) - 253*a(n-11).

G.f.: (1+x)*(1 - x^11)/(1 - 23*x + 275*x^11 - 253*x^12). (End)