cp's OEIS Frontend

A163600 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163600 #16 Sep 08 2022 08:45:46
%S A163600 1,35,1190,40460,1375640,46771165,1590199380,54066091695,
%T A163600 1838223751980,62498813135220,2124932636259510,72246791293015185,
%U A163600 2456359680805901640,83515167573569420535,2839479604449882838290,96541079403144247211340
%N A163600 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163600 The initial terms coincide with those of A170754, although the two sequences are eventually different.
%C A163600 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163600 G. C. Greubel, <a href="/A163600/b163600.txt">Table of n, a(n) for n = 0..650</a>
%H A163600 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (33, 33, 33, 33, -561).
%F A163600 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
%F A163600 a(n) = 33*a(n-1)+33*a(n-2)+33*a(n-3)+33*a(n-4)-561*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t A163600 CoefficientList[Series[(1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 29 2017 *)
%o A163600 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6)) \\ _G. C. Greubel_, Jul 29 2017
%o A163600 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6) )); // _G. C. Greubel_, Apr 28 2019
%o A163600 (Sage) ((1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%K A163600 nonn
%O A163600 0,2
%A A163600 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009