A168835 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516518, 326173191714734, 4240251492291542, 55123269399790046, 716602502197270598

Offset

0,2

Comments

The initial terms coincide with those of A170733, although the two sequences are eventually different.

First disagreement at index 20: a(20) = 20466884065256245549387, A170733(20) = 20466884065256245549478. - Klaus Brockhaus, Apr 02 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).

Formula

G.f.: (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)/(78*t^20 - 12*t^19 - 12*t^18 - 12*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).

Mathematica

With[{num=Total[2t^Range[19]]+t^20+1, den=Total[-12 t^Range[19]]+ 78t^20+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Sep 09 2012 *)

Crossrefs

Cf. A170733 (G.f.: (1+x)/(1-13*x)).

Sequence in context: A168691 A168739 A168787 * A168883 A168931 A168979

Adjacent sequences: A168832 A168833 A168834 * A168836 A168837 A168838

Keyword

nonn

Author

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

Status

approved