A169069 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset

0,2

Comments

The initial terms coincide with those of A003950, although the two sequences are eventually different.

First disagreement at index 25: a(25) = 1532649851044531315180, A003950(25) = 1532649851044531315208. - 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..19.

Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

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

Mathematica

With[{num=Total[2t^Range[24]]+t^25+1, den=Total[-6 t^Range[24]]+21t^25+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 20 2011 *)

Crossrefs

Cf. A003950 (G.f.: (1+x)/(1-7*x)).

Sequence in context: A168925 A168973 A169021 * A169117 A169165 A169213

Adjacent sequences: A169066 A169067 A169068 * A169070 A169071 A169072

Keyword

nonn

Author

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

Status

approved