A169472 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = 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.

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, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

Formula

G.f. (t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +

2*t^25 + 2*t^24 + 2*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^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27

- 25*t^26 - 25*t^25 - 25*t^24 - 25*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[32]]+t^33+1, den=Total[-25 t^Range[32]]+ 325t^33+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 03 2013 *)

Crossrefs

Sequence in context: A169328 A169376 A169424 * A169520 A169568 A170036

Adjacent sequences: A169469 A169470 A169471 * A169473 A169474 A169475

Keyword

nonn

Author

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

Status

approved