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

0,2

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

Table of n, a(n) for n=0..21.

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

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).

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 *)

Crossrefs

Sequence in context: A342807 A163922 A164365 * A165213 A165777 A166364

Adjacent sequences: A164738 A164739 A164740 * A164742 A164743 A164744

Keyword

nonn

Author

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

Status

approved