A165179 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429888071, 942237774801540, 43342937638584525, 1993775131269717660, 91713656033569169820, 4218828177321641054880, 194066096146558613709840

Offset

0,2

Comments

The initial terms coincide with those of A170766, 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 (45, 45, 45, 45, 45, 45, 45, -1035).

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)/(1035*t^8 -

45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1)

Mathematica

coxG[{8, 1035, -45}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 04 2023 *)

Crossrefs

Sequence in context: A163803 A164332 A164692 * A165703 A166308 A166441

Adjacent sequences: A165176 A165177 A165178 * A165180 A165181 A165182

Keyword

nonn

Author

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

Status

approved