A165264 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1099999945, 10999998900, 109999983555, 1099999781100, 10999997266500, 109999967220000, 1099999617750000, 10999995633000000, 109999950885000000

Offset

0,2

Comments

The initial terms coincide with those of A003953, 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..17.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, -45).

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)/(45*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t

+ 1)

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1, den=Total[-9 t^Range[8]]+45t^9+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 22 2011 *)

Crossrefs

Sequence in context: A115806 A115830 A164780 * A165796 A166369 A166551

Adjacent sequences: A165261 A165262 A165263 * A165265 A165266 A165267

Keyword

nonn

Author

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

Status

approved