A169060 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645445632, 1993775131690499072, 91713656057762957312, 4218828178657096036352, 194066096218226417672192

Offset

0,2

Comments

The initial terms coincide with those of A170766, although the two sequences are eventually different.

First disagreement at index 24: a(24) = 8232428862641605102710284483950744173511, A170766(24) = 8232428862641605102710284483950744174592. - Klaus Brockhaus, Apr 20 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 (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).

Formula

G.f.: (t^24 + 2*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)/(1035*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).

Mathematica

coxG[{24, 1035, -45}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 14 2015 *)

Crossrefs

Cf. A170766 (G.f.: (1+x)/(1-46*x)).

Sequence in context: A168916 A168964 A169012 * A169108 A169156 A169204

Adjacent sequences: A169057 A169058 A169059 * A169061 A169062 A169063

Keyword

nonn

Author

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

Status

approved