A169251 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750

Offset

0,2

Comments

The initial terms coincide with those of A170765, although the two sequences are eventually different.

First disagreement at index 28: a(28) = 19929467902629395915254561409354209899902342715, A170765(28) = 19929467902629395915254561409354209899902343750. - Klaus Brockhaus, May 24 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 (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).

Formula

G.f.: (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)/(990*t^28 - 44*t^27 - 44*t^26 - 44*t^25 - 44*t^24 - 44*t^23 - 44*t^22 - 44*t^21 - 44*t^20 - 44*t^19 - 44*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

Mathematica

coxG[{28, 990, -44}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 14 2017 *)

Crossrefs

Cf. A170765 (G.f.: (1+x)/(1-45*x)).

Sequence in context: A169059 A169107 A169203 * A169299 A169347 A169395

Adjacent sequences: A169248 A169249 A169250 * A169252 A169253 A169254

Keyword

nonn

Author

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

Status

approved