A169424 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = 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 is at index 32, the difference is 351. - Klaus Brockhaus, Jun 27 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, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

Formula

G.f.: (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^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).

G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-25*sum(k=1..31, x^k)+325*x^32).

Mathematica

With[{num=Total[2t^Range[31]]+t^32+1, den=Total[-25 t^Range[31]]+ 325t^32+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]]  (* Harvey P. Dale, Jun 18 2012 *)

Crossrefs

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

Sequence in context: A169280 A169328 A169376 * A169472 A169520 A169568

Adjacent sequences: A169421 A169422 A169423 * A169425 A169426 A169427

Keyword

nonn

Author

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

Status

approved