A164892 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386095961, 125563628736, 2134581644448, 36287887206528, 616894069776480, 10487198969713728, 178282378804864032, 3030800377118109696, 51523605347410047672

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170737, 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 (16, 16, 16, 16, 16, 16, 16, -136).

Programs

Mathematica

coxG[{8,136,-16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 06 2024 *)

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)/(136*t^8 -

16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)