The On-Line Encyclopedia of Integer Sequences (OEIS)

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A166924

Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
(history; published version)

#12 by Harvey P. Dale at Wed Apr 12 11:40:48 EDT 2023

STATUS

editing

approved

#11 by Harvey P. Dale at Wed Apr 12 11:40:45 EDT 2023

MATHEMATICA

coxG[{13, 28, -7}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 12 2023 *)

STATUS

approved

editing

#10 by Ray Chandler at Thu Nov 24 10:24:44 EST 2016

STATUS

editing

approved

#9 by Ray Chandler at Thu Nov 24 10:24:36 EST 2016

LINKS

<a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).

STATUS

approved

editing

#8 by Alois P. Heinz at Sat May 28 18:34:52 EDT 2016

STATUS

reviewed

approved

#7 by Michel Marcus at Sat May 28 17:24:54 EDT 2016

STATUS

proposed

reviewed

#6 by G. C. Greubel at Sat May 28 14:02:36 EDT 2016

STATUS

editing

proposed

#5 by G. C. Greubel at Sat May 28 14:02:28 EDT 2016

LINKS

G. C. Greubel, <a href="/A166924/b166924.txt">Table of n, a(n) for n = 0..500</a>

FORMULA

G.f. : (t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*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)/(28*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).

2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^13 - 7*t^12 - 7*t^11 - 7*t^10 -

7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)

MATHEMATICA

CoefficientList[Series[(t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*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)/(28*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 28 2016 *)

STATUS

approved

editing

#4 by N. J. A. Sloane at Sun Jul 13 09:05:39 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 16:51:32 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