A165654 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575206, 3757718396683440, 135277862279741370, 4870003042039640400, 175320109512309293280, 6311523942402895157760

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170756, 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 (35, 35, 35, 35, 35, 35, 35, 35, -630).

Programs

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-35 t^Range[8]]+ 630t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Nov 01 2011 *)

Formula

G.f. (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)/(630*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 -

35*t^2 - 35*t + 1)