A170059 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895522450, 3989613314880600050, 195491052429149402450, 9579061569028320720050, 469374016882387715282450

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170769, although the two sequences are eventually different.

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

Links

• Index entries for linear recurrences with constant coefficients, signature (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).

Programs

Mathematica

With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-48 t^Range[35]]+1176t^36+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Jan 16 2014 *)

Formula

G.f. (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)/(1176*t^36 - 48*t^35 - 48*t^34 - 48*t^33 -

48*t^32 - 48*t^31 - 48*t^30 - 48*t^29 - 48*t^28 - 48*t^27 - 48*t^26 -

48*t^25 - 48*t^24 - 48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 -

48*t^18 - 48*t^17 - 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 -

48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4

- 48*t^3 - 48*t^2 - 48*t + 1)