A169300 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = 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 29: a(29) = 1695575548257960208370995858121119507613631904711, A170766(29) = 1695575548257960208370995858121119507613631905792. - Klaus Brockhaus, Jun 03 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, 45, 45, 45, 45, 45, -1035).

Formula

G.f.: (t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*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^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*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

With[{num=Total[2t^Range[28]]+t^29+1, den=Total[-45 t^Range[28]]+ 1035t^29+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jul 21 2012 *)

Crossrefs

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

Sequence in context: A169156 A169204 A169252 * A169348 A169396 A169444

Adjacent sequences: A169297 A169298 A169299 * A169301 A169302 A169303

Keyword

nonn

Author

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

Status

approved