A169332 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155700000000000, 16474671000000000000, 494240130000000000000, 14827203900000000000000

Offset

0,2

Comments

The initial terms coincide with those of A170750, although the two sequences are eventually different.

First disagreement at index 30: a(30) = 212754169831137299999999999999999999999999535, A170750(30) = 212754169831137300000000000000000000000000000. - Klaus Brockhaus, Jun 23 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 (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).

Formula

G.f.: (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)/(435*t^30 - 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

Mathematica

With[{num=Total[2t^Range[21]]+t^22+1, den=Total[-29 t^Range[29]]+ 435t^30+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Dec 25 2011 *)

Crossrefs

Cf. A170750 (G.f.: (1+x)/(1-30*x)).

Sequence in context: A169188 A169236 A169284 * A169380 A169428 A169476

Adjacent sequences: A169329 A169330 A169331 * A169333 A169334 A169335

Keyword

nonn

Author

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

Status

approved