A168834 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622784

Offset

0,2

Comments

The initial terms coincide with those of A170732, although the two sequences are eventually different.

First disagreement at index 20: a(20) = 4153239991818098048946, A170732(20) = 4153239991818098049024. - 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 (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

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)/(66*t^20 - 11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).

Mathematica

coxG[{20, 66, -11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 28 2016 *)

Crossrefs

Cf. A170732 (G.f.: (1+x)/(1-12*x)).

Sequence in context: A168690 A168738 A168786 * A168882 A168930 A168978

Adjacent sequences: A168831 A168832 A168833 * A168835 A168836 A168837

Keyword

nonn

Author

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

Status

approved