A165173 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717439999180, 268697599934400, 10747903996064820, 429916159790145600, 17196646389507936000, 687865855496401920000, 27514634216499456000000

Offset

0,2

Comments

The initial terms coincide with those of A170760, 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 (39, 39, 39, 39, 39, 39, 39, -780).

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)/(780*t^8 -

39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1)

Mathematica

coxG[{8, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 01 2016 *)

Crossrefs

Sequence in context: A163677 A164091 A164685 * A165692 A166225 A166435

Adjacent sequences: A165170 A165171 A165172 * A165174 A165175 A165176

Keyword

nonn

Author

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

Status

approved