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, 1246704751477480105181184

Offset

0,2

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).

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).

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 *)

Prog

(Magma)
R<x>:=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
(SageMath)
def A166427_list(prec):
    P.<x> = 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
(PARI) a(n)=if(n, ([0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; -496, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31]^(n-1)*[33; 1056; 33792; 1081344; 34603008; 1107296256; 35433480192; 1133871366144; 36283883716608; 1161084278931456; 37154696925806064])[1, 1], 1) \\ Charles R Greathouse IV, Jun 08 2026
(PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)*(1+x)/(1-31*x-31*x^2-31*x^3-31*x^4-31*x^5-31*x^6-31*x^7-31*x^8-31*x^9-31*x^10+496*x^11)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A154638, A169452, A170752.

Sequence in context: A165140 A165645 A166129 * A166679 A167086 A167391

Adjacent sequences: A166424 A166425 A166426 * A166428 A166429 A166430

Keyword

nonn,easy

Author

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

Status

approved