A168894 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = 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 21: a(21) = 100499717946015091842770534100, A170744(21) = 100499717946015091842770534400. - Klaus Brockhaus, Apr 05 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, 23, -276).

Formula

G.f.: (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)/(276*t^21 - 23*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

coxG[{21, 276, -23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 19 2020 *)

Crossrefs

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

Sequence in context: A168750 A168798 A168846 * A168942 A168990 A169038

Adjacent sequences: A168891 A168892 A168893 * A168895 A168896 A168897

Keyword

nonn

Author

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

Status

approved