A168898 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176

Offset

0,2

Comments

The initial terms coincide with those of A170748, although the two sequences are eventually different.

First disagreement at index 21: a(21) = 2544243213423879646354293653098, A170748(21) = 2544243213423879646354293653504. - Klaus Brockhaus, Apr 05 2011

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

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).

Formula

G.f.: (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)/(378*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

Mathematica

With[{num=Total[2t^Range[20]]+t^21+1, den=Total[-27 t^Range[20]]+378t^21+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Mar 10 2013 *)

Crossrefs

Cf. A170748 (G.f.: (1+x)/(1-28*x)).

Sequence in context: A168754 A168802 A168850 * A168946 A168994 A169042

Adjacent sequences: A168895 A168896 A168897 * A168899 A168900 A168901

Keyword

nonn

Author

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

Status

approved