A166427 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806064, 1188950301625777152, 38046409652024328720, 1217485108864761234432, 38959523483671806394368

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170752, 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 (31,31,31,31,31,31,31,31,31,31,-496).

Crossrefs

Cf. A154638, A169452, A170752.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-32*x+527*x^11-496*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

With[{num=Total[2t^Range[10]]+t^11+1,den=Total[-31 t^Range[10]]+496t^11+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Aug 16 2011 *)
With[{p=496, q=31}, 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, 496, -31, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 25 2024 *)

SageMath

def A166427_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-32*x+527*x^11-496*x^12) ).list()
A166427_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)/(496*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).

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

a(n) = 31*Sum_{j=1..10} a(n-j) - 496*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 22*x + 527*x^11 - 496*x^12). (End)