A164969 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874401, 5638330725300, 146596598620875, 3811511557982700, 99099300347388900, 2576581804867917600, 66991126818296818800, 1741769294460722280000

Offset

0,2

Comments

The initial terms coincide with those of A170746, 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 (25, 25, 25, 25, 25, 25, 25, -325).

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)/(325*t^8 -

25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)

Mathematica

coxG[{8, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 23 2020 *)

Crossrefs

Sequence in context: A163527 A164017 A164644 * A165445 A165979 A166421

Adjacent sequences: A164966 A164967 A164968 * A164970 A164971 A164972

Keyword

nonn

Author

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

Status

approved