A169006 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000

Offset

0,2

Comments

The initial terms coincide with those of A170760, although the two sequences are eventually different.

First disagreement at index 23: a(23) = 7212796278210559999999999999999999180, A170760(23) = 7212796278210560000000000000000000000. - 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 (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).

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)/(780*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

Mathematica

coxG[{23, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 03 2019 *)

Crossrefs

Cf. A170760 (G.f.: (1+x)/(1-40*x)).

Sequence in context: A168862 A168910 A168958 * A169054 A169102 A169150

Adjacent sequences: A169003 A169004 A169005 * A169007 A169008 A169009

Keyword

nonn

Author

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

Status

approved