The On-Line Encyclopedia of Integer Sequences (OEIS)

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A163177

Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
(history; published version)

#10 by Harvey P. Dale at Tue Jul 09 19:17:08 EDT 2024

STATUS

editing

approved

#9 by Harvey P. Dale at Tue Jul 09 19:17:06 EDT 2024

MATHEMATICA

coxG[{4, 300, -24}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 09 2024 *)

STATUS

approved

editing

#8 by Alois P. Heinz at Mon Mar 23 07:06:48 EDT 2020

STATUS

proposed

approved

#7 by Jinyuan Wang at Mon Mar 23 06:57:34 EDT 2020

STATUS

editing

proposed

#6 by Jinyuan Wang at Mon Mar 23 06:57:20 EDT 2020

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, -300).

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

PROG

(PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^4 - 24*t^3 - 24*t^2 - 24*t + 1) + O(t^20)) \\ Jinyuan Wang, Mar 23 2020

STATUS

approved

editing

#5 by Ray Chandler at Wed Nov 23 15:42:59 EST 2016

STATUS

editing

approved

#4 by Ray Chandler at Wed Nov 23 15:42:56 EST 2016

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, -300).

STATUS

approved

editing

#3 by N. J. A. Sloane at Sun Jul 13 09:05:29 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

#2 by Russ Cox at Fri Mar 30 16:51:26 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

#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 26 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

DATA

1, 26, 650, 16250, 405925, 10140000, 253297200, 6327360000, 158057355300, 3948270300000, 98627731207200, 2463719204700000, 61543667742382800, 1537359871188960000, 38403225875902867200, 959311990194611040000

OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170745, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^4 - 24*t^3 - 24*t^2 - 24*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