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Revision History for A164686 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing all changes.
Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
(history; published version)
#10 by Michael De Vlieger at Thu Feb 22 17:47:46 EST 2024
STATUS

reviewed

approved

#9 by Andrew Howroyd at Thu Feb 22 14:32:57 EST 2024
STATUS

proposed

reviewed

#8 by Michel Marcus at Thu Feb 22 14:27:58 EST 2024
STATUS

editing

proposed

#7 by Michel Marcus at Thu Feb 22 14:27:54 EST 2024
LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, -820).

FORMULA

G.f. : (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).

40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)

STATUS

approved

editing

#6 by Ray Chandler at Wed Nov 23 18:04:31 EST 2016
STATUS

editing

approved

#5 by Ray Chandler at Wed Nov 23 18:04:28 EST 2016
LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, -820).

STATUS

approved

editing

#4 by N. J. A. Sloane at Sun Jul 13 09:05:31 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 16:51:30 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^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^7 - 40*t^6 -

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)^7 = I.

DATA

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504377261, 8179679432400, 335366855281920, 13750041007253040, 563751678865841760, 23113818733806664080, 947666563998666456000, 38854328956361647813980

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^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*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