A164777 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874332, 150994368, 1207952676, 9663603264, 77308680960, 618468286464, 4947737001984, 39581821698048, 316653979043052, 2533227076022832, 20265778557681300, 162125924058011088

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003951, 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 (7, 7, 7, 7, 7, 7, 7, -28).

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)/(28*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).