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.

A166325 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

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%I A166325 #16 Mar 12 2020 09:46:06
%S A166325 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A166325 33911153642450,1661646528480050,81420679895521225,
%U A166325 3989613314880480000,195491052429140580000,9579061569027744360000,469374016882352414700000
%N A166325 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166325 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A166325 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166325 G. C. Greubel, <a href="/A166325/b166325.txt">Table of n, a(n) for n = 0..500</a>
%H A166325 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (48,48,48,48,48,48,48,48,48,-1176).
%F A166325 G.f.: (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)/(1176*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
%p A166325 seq(coeff(series((1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 12 2020
%t A166325 CoefficientList[Series[(1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 09 2016 *)
%t A166325 coxG[{10, 1176, -48}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 12 2020 *)
%o A166325 (Sage)
%o A166325 def A166325_list(prec):
%o A166325     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166325     return P( (1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11) ).list()
%o A166325 A166325_list(30) # _G. C. Greubel_, Aug 10 2019
%K A166325 nonn
%O A166325 0,2
%A A166325 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009