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A163215 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%I A163215 #14 Apr 25 2024 09:16:20
%S A163215 1,32,992,30752,952816,29521920,914703360,28341043200,878114994960,
%T A163215 27207394552800,842990180666400,26119092121336800,809270367424023600,
%U A163215 25074322053313752000,776899354951763496000,24071343043338616536000
%N A163215 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163215 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A163215 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163215 G. C. Greubel, <a href="/A163215/b163215.txt">Table of n, a(n) for n = 0..665</a>
%H A163215 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, -465).
%F A163215 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%F A163215 From _G. C. Greubel_, Apr 28 2019: (Start)
%F A163215 a(n) = 30*(a(n-1) + a(n-2) + a(n-3)) - 465*a(n-4).
%F A163215 G.f.: (1+x)*(1-x^4)/(1 - 31*x + 495*x^4 - 465*x^5). (End)
%t A163215 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(465*t^4-30*t^3-30*t^2 - 30*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{30, 30, 30, -465}, {1, 32,992,30752,952816}, 20] (* _G. C. Greubel_, Dec 10 2016 *)
%o A163215 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)) \\ _G. C. Greubel_, Dec 10 2016, modified Apr 28 2019
%o A163215 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5) )); // _G. C. Greubel_, Apr 28 2019
%o A163215 (Sage) ((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%o A163215 (GAP) a:=[32,992,30752,952816];; for n in [5..20] do a[n]:=30*(a[n-1]+a[n-2] +a[n-3]) -465*a[n-4]; od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019
%K A163215 nonn
%O A163215 0,2
%A A163215 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009