A168917 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696

Offset

0,2

Comments

The initial terms coincide with those of A170767, although the two sequences are eventually different.

First disagreement at index 21: a(21) = 132800098174192118853635904544434120, A170767(21) = 132800098174192118853635904544435248. - Klaus Brockhaus, Apr 08 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 (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).

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)/(1081*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

Mathematica

coxG[{21, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 02 2014 *)

Crossrefs

Cf. A170767 (G.f.: (1+x)/(1-47*x)).

Sequence in context: A168773 A168821 A168869 * A168965 A169013 A169061

Adjacent sequences: A168914 A168915 A168916 * A168918 A168919 A168920

Keyword

nonn

Author

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

Status

approved