The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A168688

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A168688

Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
(history; published version)

#18 by Susanna Cuyler at Wed Mar 24 08:06:00 EDT 2021

STATUS

reviewed

approved

#17 by Michel Marcus at Wed Mar 24 04:23:05 EDT 2021

STATUS

proposed

reviewed

#16 by Jon E. Schoenfield at Wed Mar 24 01:16:32 EDT 2021

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Wed Mar 24 01:16:30 EDT 2021

CROSSREFS

Cf. A003953 (Gg.f.: (1+x)/(1-10*x)).

#14 by Jon E. Schoenfield at Wed Mar 24 01:16:08 EDT 2021

COMMENTS

First disagreement at index 17: a(17) = 109999999999999945, A003953(17) = 110000000000000000. - _Klaus Brockhaus, _, Mar 30 2011

FORMULA

G.f.: (1+t)*(1-t^17)/(1 - 10*t + 54*t^17 -454 5*t^18). - G. C. Greubel, Mar 24 2021

STATUS

proposed

editing

#13 by G. C. Greubel at Wed Mar 24 00:45:05 EDT 2021

STATUS

editing

proposed

#12 by G. C. Greubel at Wed Mar 24 00:44:51 EDT 2021

LINKS

<a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

FORMULA

G.f.: (1+t)*(1-t^17)/(1 -10*t +54*t^17 -45*t^18). - G. C. Greubel, Mar 24 2021

MATHEMATICA

CoefficientList[Series[(t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*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)/(45*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 03 2016 *)

CoefficientList[Series[(1+t)*(1-t^17)/(1 -10*t +54*t^17 -45*t^18), {t, 0, 50}], t] (* G. C. Greubel, Aug 03 2016; Mar 24 2021 *)

coxG[{17, 45, -9, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 24 2021 *)

PROG

(Magma)

R<t>:=PowerSeriesRing(Integers(), 40);

Coefficients(R!( (1+t)*(1-t^17)/(1 -10*t +54*t^17 -45*t^18) )); // G. C. Greubel, Mar 24 2021

(Sage)

def A168688_list(prec):

P.<t> = PowerSeriesRing(ZZ, prec)

return P( (1+t)*(1-t^17)/(1 -10*t +54*t^17 -45*t^18) ).list()

A168688_list(40) # G. C. Greubel, Mar 24 2021

STATUS

approved

editing

#11 by Ray Chandler at Thu Nov 24 13:01:57 EST 2016

STATUS

editing

approved

#10 by Ray Chandler at Thu Nov 24 13:01:54 EST 2016

LINKS

<a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

STATUS

approved

editing

#9 by Bruno Berselli at Wed Aug 03 12:24:24 EDT 2016

STATUS

proposed

approved