A166877 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593750, 292968750, 1464843735, 7324218600, 36621092640, 183105461400, 915527298000, 4577636445000, 22888182000000, 114440908875000, 572204538750000

Offset

0,2

Comments

The initial terms coincide with those of A003948, 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 (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).

Formula

G.f.: (t^13 + 2*t^12 + 2*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)/(10*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).

Mathematica

With[{num=Total[2t^Range[12]]+t^13+1, den=Total[-4 t^Range[12]]+ 10t^13+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jul 27 2011 *)
CoefficientList[Series[(t^13 + 2*t^12 + 2*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)/(10*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 27 2016 *)

Crossrefs

Sequence in context: A165777 A166364 A166500 * A167107 A167651 A167897

Adjacent sequences: A166874 A166875 A166876 * A166878 A166879 A166880

Keyword

nonn

Author

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

Status

approved