%I #14 Oct 07 2024 01:32:11

%S 1,11,110,1100,10945,108900,1083555,10781100,107269470,1067306625,

%T 10619454780,105661128375,1051303881870,10460231387100,

%U 104076892111005,1035541095642900,10303395297584895,102516409155629700,1020014649794722230,10148910738927500925

%N 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 The initial terms coincide with those of A003953, although the two sequences are eventually different.

%C Computed with Magma using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A162987/b162987.txt">Table of n, a(n) for n = 0..995</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,9,9,-45).

%F 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 From _G. C. Greubel_, Apr 28 2019: (Start)

%F a(n) = 9*(a(n-1) + a(n-2) + a(n-3) - 5*a(n-4)).

%F G.f.: (1+x)*(1-x^4)/(1 - 10*x + 54*x^4 - 45*x^5). (End)

%t 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 (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 (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 (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 (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 nonn,easy

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009