A165269 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589761970, 67077142704, 804925701294, 9659108281680, 115909297773984, 1390911554013696, 16690938416875008, 200291258227027968

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, 11, -66).

Programs

Mathematica

coxG[{9,66,-11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 03 2022 *)

Formula

G.f. (t^9 + 2*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^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 -

11*t^2 - 11*t + 1)