A165692 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697599999180, 10747903999934400, 429916159996064820, 17196646399790145600, 687865855989507936000, 27514634239496401920000

Offset

0,2

Comments

The initial terms coincide with those of A170760, 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..14.

Index entries for linear recurrences with constant coefficients, signature (39, 39, 39, 39, 39, 39, 39, 39, -780).

Formula

G.f. (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)/(780*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 -

39*t^2 - 39*t + 1)

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1, den=Total[-39 t^Range[8]]+ 780t^9+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jul 20 2011 *)

Crossrefs

Sequence in context: A164091 A164685 A165173 * A166225 A166435 A166714

Adjacent sequences: A165689 A165690 A165691 * A165693 A165694 A165695

Keyword

nonn

Author

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

Status

approved