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

Author

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

Keywords

• nonn

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

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

Programs

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 *)

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)