A168846 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset

0,2

Comments

The initial terms coincide with those of A170744, although the two sequences are eventually different.

First disagreement at index 20: a(20) = 4187488247750628826782105300, A170744(20) = 4187488247750628826782105600. - Klaus Brockhaus, Apr 02 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Formula

G.f.: (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)/(276*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

Mathematica

With[{num=Total[2t^Range[19]]+t^20+1, den=Total[-23 t^Range[19]]+ 276t^20+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jul 20 2011 *)

Crossrefs

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

Sequence in context: A168702 A168750 A168798 * A168894 A168942 A168990

Adjacent sequences: A168843 A168844 A168845 * A168847 A168848 A168849

Keyword

nonn

Author

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

Status

approved