A164085 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967180, 140749689600, 5489236708800, 214080185404800, 8349125427489600, 325615821343488000, 12699014289580990020, 495261450323895092760, 19315192390812032456040

Offset

0,2

Comments

The initial terms coincide with those of A170759, 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 (38,38,38,38,38,-741).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

Mathematica

coxG[{6, 741, -38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 23 2021 *)

Crossrefs

Sequence in context: A162877 A163223 A163669 * A164684 A165172 A165690

Adjacent sequences: A164082 A164083 A164084 * A164086 A164087 A164088

Keyword

nonn

Author

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

Status

approved