A164815 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813426, 5589760176, 67077110958, 804925197648, 9659100765600, 115909189913088, 1390910047667712, 16690917796540416, 200290980252825462

Offset

0,2

Comments

The initial terms coincide with those of A170732, 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..16.

Index entries for linear recurrences with constant coefficients, signature (11,11,11,11,11,11,11,-66).

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)/(66*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1)

Mathematica

With[{num=Total[2t^Range[7]]+t^8+1, den=Total[-11 t^Range[7]]+66t^8+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Aug 21 2011 *)

Crossrefs

Sequence in context: A163438 A163958 A164610 * A165269 A165873 A166377

Adjacent sequences: A164812 A164813 A164814 * A164816 A164817 A164818

Keyword

nonn

Author

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

Status

approved