A163439 - OEIS

%I #20 Sep 08 2022 08:45:46

%S 1,14,182,2366,30758,399763,5195736,67529280,877681896,11407280976,

%T 148261073142,1926957516120,25044775341768,325508355356184,

%U 4230650423530440,54986001777229068,714656161291232160

%N Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%C The initial terms coincide with those of A170733, 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="/A163439/b163439.txt">Table of n, a(n) for n = 0..895</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, -78).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(78*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).

%F a(n) = 12*a(n-1)+12*a(n-2)+12*a(n-3)+12*a(n-4)-78*a(n-5). - _Wesley Ivan Hurt_, May 10 2021

%t CoefficientList[Series[(1+x)*(1-x^5)/(1-13*x+90*x^5-78*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{12, 12, 12, 12, -78}, {1, 14, 182, 2366, 30758, 399763}, 30]] (* _G. C. Greubel_, Dec 23 2016 *)

%t coxG[{5, 78, -12}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 12 2019 *)

%o (PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-13*x+90*x^5-78*x^6)) \\ _G. C. Greubel_, Dec 23 2016

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-13*x+90*x^5-78*x^6) )); // _G. C. Greubel_, May 12 2019

%o (Sage) ((1+x)*(1-x^5)/(1-13*x+90*x^5-78*x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 12 2019

%K nonn

%O 0,2

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