A168704 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

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

Offset: 0

Author

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

Keywords

• nonn

Comments

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

First disagreement at index 17: a(17) = 1177436058284579599613601, A170746(17) = 1177436058284579599613952. - Klaus Brockhaus, Mar 30 2011

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..499
• 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, -325).

Crossrefs

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

Programs

Mathematica

CoefficientList[Series[(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^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), {t,0,50}], t] (* G. C. Greubel, Aug 04 2016 *)
coxG[{17,325,-25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 03 2020 *)

Formula

G.f.: (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^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).