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A165693

Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
(history; published version)

#8 by Harvey P. Dale at Sun Nov 05 09:37:54 EST 2017

STATUS

editing

approved

#7 by Harvey P. Dale at Sun Nov 05 09:37:50 EST 2017

MATHEMATICA

coxG[{9, 820, -40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 05 2017 *)

STATUS

approved

editing

#6 by Ray Chandler at Wed Nov 23 22:17:20 EST 2016

STATUS

editing

approved

#5 by Ray Chandler at Wed Nov 23 22:17:18 EST 2016

LINKS

<a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, -820).

STATUS

approved

editing

#4 by N. J. A. Sloane at Sun Jul 13 09:05:33 EDT 2014

AUTHOR

_John Cannon (john(AT)maths.usyd.edu.au) _ and N. J. A. Sloane, Dec 03 2009

Discussion

Sun Jul 13

09:05

OEIS Server: https://oeis.org/edit/global/2246

#3 by Russ Cox at Fri Mar 30 16:51:31 EDT 2012

AUTHOR

John Cannon (john(AT)maths.usyd.edu.au) and _N. J. A. Sloane (njas(AT)research.att.com), _, Dec 03 2009

Discussion

Fri Mar 30

16:51

OEIS Server: https://oeis.org/edit/global/110

#2 by N. J. A. Sloane at Sun Jul 11 03:00:00 EDT 2010

FORMULA

G,.f.: (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

DATA

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859622221, 13750041244475760, 563751691022059680, 23113819331845141200, 947666592603219256320, 38854330296632296661040

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.

FORMULA

G,f.: (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

1)/(820*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 -

40*t^2 - 40*t + 1)

KEYWORD

nonn

AUTHOR

John Cannon (john(AT)maths.usyd.edu.au) and N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2009

STATUS

approved