A169015 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895522450, 3989613314880600050, 195491052429149402450, 9579061569028320720050, 469374016882387715282450

Offset

0,2

Comments

The initial terms coincide with those of A170769, although the two sequences are eventually different.

First disagreement at index 23: a(23) = 764335031597128809688259288463841318825, A170769(23) = 764335031597128809688259288463841320050. - 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 (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).

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)/(1176*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 - 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).

Mathematica

With[{num=Total[2t^Range[22]]+t^23+1, den=Total[-48 t^Range[22]]+1176t^23+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Feb 27 2012 *)

Crossrefs

Cf. A170769 (G.f.: (1+x)/(1-49*x)).

Sequence in context: A168871 A168919 A168967 * A169063 A169111 A169159

Adjacent sequences: A169012 A169013 A169014 * A169016 A169017 A169018

Keyword

nonn

Author

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

Status

approved