A168992 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = 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 23: a(23) = 363728573635362135848513282506401, A170746(23) = 363728573635362135848513282506752. - Klaus Brockhaus, Apr 19 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, 25, 25, 25, -325).

Formula

G.f.: (t^23 + 2*t^22 + 2*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)/(325*t^23 - 25*t^22 - 25*t^21 - 25*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

With[{num=Total[2t^Range[22]]+t^23+1, den=Total[-25 t^Range[22]]+ 325t^23+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Dec 10 2012 *)

Crossrefs

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

Sequence in context: A168848 A168896 A168944 * A169040 A169088 A169136

Adjacent sequences: A168989 A168990 A168991 * A168993 A168994 A168995

Keyword

nonn

Author

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

Status

approved