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

0,2

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

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (35, 35, 35, 35, 35, 35, 35, 35, -630).

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)

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 *)

Crossrefs

Sequence in context: A164070 A164673 A165169 * A166167 A166431 A166689

Adjacent sequences: A165651 A165652 A165653 * A165655 A165656 A165657

Keyword

nonn

Author

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

Status

approved