A164637 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861060, 81715798032, 1879463209008, 43227650455440, 994235883385008, 22867423544782608, 525950700749330736, 12096865179279290124, 278227877550453062232

Offset

0,2

Comments

The initial terms coincide with those of A170743, 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..15.

Index entries for linear recurrences with constant coefficients, signature (22,22,22,22,22,22,-253).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

Mathematica

coxG[{7, 253, -22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 05 2022 *)

Crossrefs

Sequence in context: A163174 A163519 A163992 * A164959 A165366 A165965

Adjacent sequences: A164634 A164635 A164636 * A164638 A164639 A164640

Keyword

nonn

Author

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

Status

approved