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

Author

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

Keywords

• nonn

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

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

Programs

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 *)

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)