A169101 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407664040, 12699033492898897560, 495262306223057004840, 19315229942699223188760

Offset

0,2

Comments

The initial terms coincide with those of A170759, although the two sequences are eventually different.

First disagreement at index 25: a(25) = 6132118799134527230569438737204794584860, A170759(25) = 6132118799134527230569438737204794585640. - 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 (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).

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)/(741*t^25 - 38*t^24 - 38*t^23 - 38*t^22 - 38*t^21 - 38*t^20 - 38*t^19 - 38*t^18 - 38*t^17 - 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

Crossrefs

Cf. A170759 (G.f.: (1+x)/(1-39*x)).

Sequence in context: A168957 A169005 A169053 * A169149 A169197 A169245

Adjacent sequences: A169098 A169099 A169100 * A169102 A169103 A169104

Keyword

nonn

Author

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

Status

approved