A169347 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = 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 30: a(30) = 40357172502824526728390486853942275047302246092715, A170765(30) = 40357172502824526728390486853942275047302246093750. - Klaus Brockhaus, Jun 23 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, 44, 44, -990).

Formula

G.f.: (t^30 + 2*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)/(990*t^30 - 44*t^29 - 44*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[{30, 990, -44}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 26 2024 *)

Crossrefs

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

Sequence in context: A169203 A169251 A169299 * A169395 A169443 A169491

Adjacent sequences: A169344 A169345 A169346 * A169348 A169349 A169350

Keyword

nonn,changed

Author

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

Status

approved