A169048 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset

0,2

Comments

The initial terms coincide with those of A170754, although the two sequences are eventually different.

First disagreement at index 24: a(24) = 5862503787780549288621808968940912045, A170754(24) = 5862503787780549288621808968940912640. - Klaus Brockhaus, Apr 20 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 (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

Formula

G.f.: (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)/(561*t^24 - 33*t^23 - 33*t^22 - 33*t^21 - 33*t^20 - 33*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

Mathematica

With[{num=Total[2t^Range[23]]+t^24+1, den=Total[-33 t^Range[23]]+561t^24+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, May 05 2014 *)

Crossrefs

Cf. A170754 (G.f.: (1+x)/(1-34*x)).

Sequence in context: A168904 A168952 A169000 * A169096 A169144 A169192

Adjacent sequences: A169045 A169046 A169047 * A169049 A169050 A169051

Keyword

nonn

Author

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

Status

approved