A162744 - OEIS

A162744

Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 7, 42, 231, 1260, 6825, 36960, 200025, 1082550, 5858475, 31704750, 171577875, 928536000, 5024998125, 27194002500, 147166963125, 796429856250, 4310074059375, 23325015131250, 126228998109375, 683118955312500

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003949, 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..20.

Index entries for linear recurrences with constant coefficients, signature (5, 5, -15).

FORMULA

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(15*t^3 - 5*t^2 - 5*t + 1)

MATHEMATICA

coxG[{3, 15, -5}] (* The coxG program is at A169452 *) (* or *) LinearRecurrence[{5, 5, -15}, {1, 7, 42, 231}, 30] (* Harvey P. Dale, Oct 02 2021 *)

CROSSREFS

Sequence in context: A349427 A200864 A279613 * A324945 A164072 A111995

Adjacent sequences: A162741 A162742 A162743 * A162745 A162746 A162747

KEYWORD

nonn

AUTHOR

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

STATUS

approved