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A162987 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%I A162987 #14 Oct 07 2024 01:32:11
%S A162987 1,11,110,1100,10945,108900,1083555,10781100,107269470,1067306625,
%T A162987 10619454780,105661128375,1051303881870,10460231387100,
%U A162987 104076892111005,1035541095642900,10303395297584895,102516409155629700,1020014649794722230,10148910738927500925
%N A162987 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A162987 The initial terms coincide with those of A003953, although the two sequences are eventually different.
%C A162987 Computed with Magma using commands similar to those used to compute A154638.
%H A162987 G. C. Greubel, <a href="/A162987/b162987.txt">Table of n, a(n) for n = 0..995</a>
%H A162987 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,9,9,-45).
%F A162987 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
%F A162987 From _G. C. Greubel_, Apr 28 2019: (Start)
%F A162987 a(n) = 9*(a(n-1) + a(n-2) + a(n-3) - 5*a(n-4)).
%F A162987 G.f.: (1+x)*(1-x^4)/(1 - 10*x + 54*x^4 - 45*x^5). (End)
%t A162987 CoefficientList[Series[(1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5), {x,0,20}], x] (* or *) coxG[{4, 45, -9}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 28 2019 *)
%o A162987 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)) \\ _G. C. Greubel_, Apr 28 2019
%o A162987 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5) )); // _G. C. Greubel_, Apr 28 2019
%o A162987 (Sage) ((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%o A162987 (GAP) a:=[11,110,1100,10945];; for n in [5..20] do a[n]:=9*(a[n-1]+a[n-2] +a[n-3] -5*a[n-4]); od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019
%K A162987 nonn,easy
%O A162987 0,2
%A A162987 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009