A169005 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = 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 23: a(23) = 4031636291344199362636054396584348060, A170759(23) = 4031636291344199362636054396584348840. - Klaus Brockhaus, Apr 19 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, -741).

Formula

G.f.: (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^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).

Mathematica

coxG[{23, 741, -38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 28 2024 *)

Crossrefs

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

Sequence in context: A168861 A168909 A168957 * A169053 A169101 A169149

Adjacent sequences: A169002 A169003 A169004 * A169006 A169007 A169008

Keyword

nonn

Author

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

Status

approved