A169109 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696

Offset

0,2

Comments

The initial terms coincide with those of A170767, although the two sequences are eventually different.

First disagreement at index 25: a(25) = 648022115858739972719828904323294335394760, A170767(25) = 648022115858739972719828904323294335395888. - Klaus Brockhaus, Apr 25 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).

Formula

G.f.: (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)/(1081*t^25 - 46*t^24 - 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

Mathematica

With[{num=Total[2t^Range[24]]+t^25+1, den=Total[-46 t^Range[24]]+1081t^25+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Apr 01 2014 *)

Crossrefs

Cf. A170767 (G.f.: (1+x)/(1-47*x)).

Sequence in context: A168965 A169013 A169061 * A169157 A169205 A169253

Adjacent sequences: A169106 A169107 A169108 * A169110 A169111 A169112

Keyword

nonn

Author

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

Status

approved