A168848 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352

Offset

0,2

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.

First disagreement at index 20: a(20) = 20694616160409771042814820001, A170746(20) = 20694616160409771042814820352. - 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..15.

Index entries for linear recurrences with constant coefficients, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

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)/(325*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

Mathematica

coxG[{20, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 28 2022 *)

Crossrefs

Cf. A170746 (G.f.: (1+x)/(1-26*x)).

Sequence in context: A168704 A168752 A168800 * A168896 A168944 A168992

Adjacent sequences: A168845 A168846 A168847 * A168849 A168850 A168851

Keyword

nonn

Author

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

Status

approved