A165168 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214686870, 81067514018400, 2837362989872880, 99307704618561600, 3475769660705034000, 121651938091614420000, 4257817832049342750000, 149023624081226328000000

Offset

0,2

Comments

The initial terms coincide with those of A170755, 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 (34, 34, 34, 34, 34, 34, 34, -595).

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)/(595*t^8 -

34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1)

Mathematica

coxG[{8, 595, -34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 08 2020 *)

Crossrefs

Sequence in context: A163601 A164069 A164672 * A165651 A166165 A166430

Adjacent sequences: A165165 A165166 A165167 * A165169 A165170 A165171

Keyword

nonn

Author

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

Status

approved