A169312 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset

0,2

Comments

The initial terms coincide with those of A003953, although the two sequences are eventually different.

First disagreement at index 30: a(30) = 1099999999999999999999999999945, A003953(30) = 1100000000000000000000000000000. - Klaus Brockhaus, Jun 22 2011

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, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Formula

G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*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^30 - 9*t^29 - 9*t^28 - 9*t^27 - 9*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*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[29]]+t^30+1, den=Total[-9 t^Range[29]]+ 45t^30+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Oct 13 2012 *)

Crossrefs

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

Sequence in context: A169168 A169216 A169264 * A169360 A169408 A169456

Adjacent sequences: A169309 A169310 A169311 * A169313 A169314 A169315

Keyword

nonn

Author

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

Status

approved