A165177 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501433890, 632170063047600, 27815482772178750, 1223881241891576400, 53850774639520663200, 2369434083975726451200, 104255099687751923750400

Offset

0,2

Comments

The initial terms coincide with those of A170764, 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..14.

Index entries for linear recurrences with constant coefficients, signature (43, 43, 43, 43, 43, 43, 43, -946).

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)/(946*t^8 -

43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)

Mathematica

coxG[{8, 946, -43}] (* The coxG program is at A169452 *)  (* Harvey P. Dale, May 18 2023 *)

Crossrefs

Sequence in context: A163749 A164330 A164690 * A165699 A166258 A166439

Adjacent sequences: A165174 A165175 A165176 * A165178 A165179 A165180

Keyword

nonn

Author

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

Status

approved