A170727 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = 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.

Computed with MAGMA using commands similar to those used to compute A154638.

About the initial comment, first disagreement is at index 50 and the difference is 1035. - Vincenzo Librandi, Dec 08 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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, 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^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +

2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +

2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*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^50 - 44*t^49 - 44*t^48 - 44*t^47 - 44*t^46 - 44*t^45 -

44*t^44 - 44*t^43 - 44*t^42 - 44*t^41 - 44*t^40 - 44*t^39 - 44*t^38 -

44*t^37 - 44*t^36 - 44*t^35 - 44*t^34 - 44*t^33 - 44*t^32 - 44*t^31 -

44*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).

From Zak Seidov, Dec 04 2009: (Start)

G.f.: (t^50+2f+1)/(990*t^50-44f+1) with f=t*(1+t+t^2+t^3+t^4+t^5+t^6)*(1+t^7+t^14+t^21+t^28+t^35+t^42).

G.f.: (1 + t - t^50 - t^51)/(1 - 45*t + 1034*t^50 - 990*t^51).

(End)

Mathematica

With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-44 t^Range[49]] + 990t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 2012 *)
coxG[{50, 990, -44}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 14 2022 *)

Crossrefs

Sequence in context: A170583 A170631 A170679 * A170765 A218748 A158752

Adjacent sequences: A170724 A170725 A170726 * A170728 A170729 A170730

Keyword

nonn

Author

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

Status

approved