A164959 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810452, 1879463634048, 43227663437376, 994236255707904, 22867433804191680, 525950975723336064, 12096872400856060224, 278228064281733992448

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, 22, -253).

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)/(253*t^8 -

22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1)

Mathematica

coxG[{8, 253, -22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 20 2023 *)

Crossrefs

Sequence in context: A163519 A163992 A164637 * A165366 A165965 A166418

Adjacent sequences: A164956 A164957 A164958 * A164960 A164961 A164962

Keyword

nonn

Author

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

Status

approved