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%I #19 Sep 08 2022 08:45:46
%S 1,29,812,22736,636608,17824618,499077936,13973864310,391259299536,
%T 10955011154976,306733334006862,8588337963333660,240467992209756738,
%U 6732950603977585764,188518328027869860720,5278393098774299901978
%N Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A170748, 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="/A163549/b163549.txt">Table of n, a(n) for n = 0..685</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, -378).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
%F a(n) = 27*a(n-1)+27*a(n-2)+27*a(n-3)+27*a(n-4)-378*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)
%t coxG[{5, 378, -27}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6)) \\ _G. C. Greubel_, Jul 27 2017
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6) )); // _G. C. Greubel_, May 16 2019
%o (Sage) ((1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K nonn,easy
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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