A164741 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468735, 2343600, 11717640, 58586400, 292923000, 1464570000, 7322625000, 36612000000, 183054375210, 915243753000, 4576078154040, 22879687737000, 114394923627000, 571957043385000

Offset: 0

Author

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

Keywords

• nonn

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

• Index entries for linear recurrences with constant coefficients, signature (4, 4, 4, 4, 4, 4, 4, -10).

Programs

Mathematica

With[{num=Total[2t^Range[7]]+t^8+1, den=Total[-4 t^Range[7]]+10t^8+1}, CoefficientList[Series[num/den,{t,0,25}],t]] (* Harvey P. Dale, Jul 14 2011 *)

Formula

G.f.: (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^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).