A169337 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500

Offset

0,2

Comments

The initial terms coincide with those of A170755, although the two sequences are eventually different.

First disagreement at index 30: a(30) = 21591150613366527513815807551145553588867186870, A170755(30) = 21591150613366527513815807551145553588867187500. - 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 (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).

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)/(595*t^30 - 34*t^29 - 34*t^28 - 34*t^27 - 34*t^26 - 34*t^25 - 34*t^24 - 34*t^23 - 34*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

Mathematica

With[{num=Total[2t^Range[29]]+t^30+1, den=Total[-34 t^Range[29]]+595t^30+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Apr 12 2013 *)

Crossrefs

Cf. A170755 (G.f.: (1+x)/(1-35*x)).

Sequence in context: A169193 A169241 A169289 * A169385 A169433 A169481

Adjacent sequences: A169334 A169335 A169336 * A169338 A169339 A169340

Keyword

nonn

Author

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

Status

approved