A164696 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 3, 6, 12, 24, 48, 96, 192, 381, 756, 1503, 2988, 5940, 11808, 23472, 46656, 92742, 184353, 366456, 728439, 1447986, 2878296, 5721456, 11373072, 22607316, 44938668, 89328777, 177567132, 352966731, 701624856, 1394685096, 2772345504

Offset

0,2

Comments

The initial terms coincide with those of A003945, 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..31.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1, -1).

Formula

G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1).

Mathematica

With[{num=Total[2t^Range[7]]+t^8+1, den=Total[-t^Range[7]]+t^8+1}, CoefficientList[ Series[ num/den, {t, 0, 40}], t]] (* Harvey P. Dale, Aug 05 2011 *)

Crossrefs

Sequence in context: A115829 A115805 A356040 * A344040 A165183 A046944

Adjacent sequences: A164693 A164694 A164695 * A164697 A164698 A164699

Keyword

nonn

Author

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

Status

approved