A163225 - OEIS

A163225

Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 42, 1722, 70602, 2893821, 118611360, 4861619280, 199267084800, 8167519684380, 334768674223200, 13721431911885600, 562411325222191200, 23052003666190808400, 944850946620132384000, 38727362890294069152000

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170761, 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 (40, 40, 40, -820).

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)

MATHEMATICA

coxG[{4, 820, -40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 22 2026 *)

CROSSREFS

Sequence in context: A004997 A120815 A162879 * A163743 A164112 A164686

Adjacent sequences: A163222 A163223 A163224 * A163226 A163227 A163228

KEYWORD

nonn

AUTHOR

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

STATUS

approved