A163397 - OEIS

%I #15 Sep 08 2022 08:45:46

%S 1,10,90,810,7290,65565,589680,5303520,47699280,429001920,3858394860,

%T 34701968160,312105587040,2807042441760,25246223065440,

%U 227061682284240,2042167156174080,18367021030590720,165190915209012480

%N Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%C The initial terms coincide with those of A003952, 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="/A163397/b163397.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8, 8, 8, 8, -36).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

%F a(n) = 8*a(n-1)+8*a(n-2)+8*a(n-3)+8*a(n-4)-36*a(n-5). - _Wesley Ivan Hurt_, May 10 2021

%t CoefficientList[Series[(1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{8,8,8,8,-36}, {1,10,90,810,7290,65565}, 30] (* _G. C. Greubel_, Dec 21 2016 *)

%t coxG[{5, 36, -8}] (* 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)/(1-9*x+44*x^5-36*x^6)) \\ _G. C. Greubel_, Dec 21 2016

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6) )); // _G. C. Greubel_, May 12 2019

%o (Sage) ((1+x)*(1-x^5)/(1-9*x+44*x^5-36*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