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A163216 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%I A163216 #15 Apr 25 2024 09:16:32
%S A163216 1,33,1056,33792,1080816,34569216,1105674768,35364307968,
%T A163216 1131105025776,36177678932736,1157120181575952,37009757234816256,
%U A163216 1183733679862288368,37860973146888460800,1210959282493490855952,38731766829339020895744
%N A163216 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163216 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A163216 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163216 G. C. Greubel, <a href="/A163216/b163216.txt">Table of n, a(n) for n = 0..660</a>
%H A163216 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, -496).
%F A163216 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(496*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
%F A163216 From _G. C. Greubel_, Apr 28 2019: (Start)
%F A163216 a(n) = 31*(a(n-1) + a(n-2) + a(n-3) - 16*a(n-4)).
%F A163216 G.f.: (1+x)*(1-x^4)/(1 - 32*x + 527*x^4 - 496*x^5). (End)
%t A163216 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(496*t^4-31*t^3-31*t^2 - 31*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{31,31,31,-496}, {1,33, 1056,33792,1080816}, 20] (* _G. C. Greubel_, Dec 11 2016 *)
%t A163216 coxG[{4, 496, -31}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 28 2019 *)
%o A163216 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-32*x+527*x^4-496*x^5)) \\ _G. C. Greubel_, Dec 11 2016, modified Apr 28 2019
%o A163216 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-32*x+527*x^4-496*x^5) )); // _G. C. Greubel_, Apr 28 2019
%o A163216 (Sage) ((1+x)*(1-x^4)/(1-32*x+527*x^4-496*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%o A163216 (GAP) a:=[33,1056,33792,1080816];; for n in [5..20] do a[n]:=31*(a[n-1]+ a[n-2]+a[n-3]-16*a[n-4]); od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019
%K A163216 nonn
%O A163216 0,2
%A A163216 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009