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%I #16 Sep 08 2022 08:45:46
%S 1,12,132,1452,15972,175626,1931160,21234840,233496120,2567499000,
%T 28231951770,310435603500,3413517587700,37534684133100,
%U 412727480315700,4538308419052650,49902767052699000,548725632894681000
%N Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A003954, 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="/A163432/b163432.txt">Table of n, a(n) for n = 0..950</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10, 10, 10, 10, -55).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
%F a(n) = 10*a(n-1)+10*a(n-2)+10*a(n-3)+10*a(n-4)-55*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{10,10,10,10,-55}, {1,12,132,1452,15972, 175626}, 30] (* _G. C. Greubel_, Dec 23 2016 *)
%t coxG[{5, 55, -10}] (* 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)/(1-11*x+65*x^5-55*x^6)) \\ _G. C. Greubel_, Dec 23 2016
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6) )); // _G. C. Greubel_, May 12 2019
%o (Sage) ((1+x)*(1-x^5)/(1-11*x+65*x^5-55*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
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