A168993 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852

Offset

0,2

Comments

The initial terms coincide with those of A170747, although the two sequences are eventually different.

First disagreement at index 23: a(23) = 865288322713713146133777970498434, A170747(23) = 865288322713713146133777970498812. - 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..15.

Index entries for linear recurrences with constant coefficients, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

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)/(351*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

Mathematica

With[{num=Total[2t^Range[22]]+t^23+1, den=Total[-26 t^Range[22]]+ 351t^23+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, May 01 2012 *)

Crossrefs

Cf. A170747 (G.f.: (1+x)/(1-27*x)).

Sequence in context: A168849 A168897 A168945 * A169041 A169089 A169137

Adjacent sequences: A168990 A168991 A168992 * A168994 A168995 A168996

Keyword

nonn

Author

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

Status

approved