cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A166331 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

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%I A166331 #14 Mar 13 2020 08:38:20
%S A166331 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242870,20971440,
%T A166331 83885610,335541840,1342164960,5368650240,21474562560,85898096640,
%U A166331 343591772160,1374364631040,5497448693760,21989755453530,87958864528380
%N A166331 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166331 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A166331 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166331 G. C. Greubel, <a href="/A166331/b166331.txt">Table of n, a(n) for n = 0..1000</a>
%H A166331 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,3,3,3,3,3,3,3,3,-6).
%F A166331 G.f.: (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)/(6*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
%p A166331 seq(coeff(series((1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 13 2020
%t A166331 CoefficientList[Series[(1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12), {t,0,30}], t] (* _G. C. Greubel_, May 09 2016 *)
%t A166331 coxG[{11, 6, -3}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 13 2020 *)
%o A166331 (Sage)
%o A166331 def A166331_list(prec):
%o A166331     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166331     return P( (1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12) ).list()
%o A166331 A166331_list(30) # _G. C. Greubel_, Mar 13 2020
%K A166331 nonn
%O A166331 0,2
%A A166331 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009