A170717 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500

Offset

0,2

Comments

The initial terms coincide with those of A170755, 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 630. - Vincenzo Librandi, Dec 06 2012

Links

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

Index entries for linear recurrences with constant coefficients, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).

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)/(595*t^50 - 34*t^49 - 34*t^48 - 34*t^47 - 34*t^46 - 34*t^45 -

34*t^44 - 34*t^43 - 34*t^42 - 34*t^41 - 34*t^40 - 34*t^39 - 34*t^38 -

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

34*t^30 - 34*t^29 - 34*t^28 - 34*t^27 - 34*t^26 - 34*t^25 - 34*t^24 -

34*t^23 - 34*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 -

34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 -

34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 -

34*t + 1).

Mathematica

With[{num = Total[2 t^Range[49]]+ t^50 + 1, den = Total[-34  t^Range[49]] + 595 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 06 2012 *)
coxG[{50, 595, -34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 05 2018 *)

Crossrefs

Sequence in context: A170573 A170621 A170669 * A170755 A218738 A158700

Adjacent sequences: A170714 A170715 A170716 * A170718 A170719 A170720

Keyword

nonn

Author

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

Status

approved