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%I #20 Sep 08 2022 08:45:46
%S 1,28,756,20412,551124,14879970,401748984,10846947384,292860149400,
%T 7907023424664,213484216161762,5763927599870076,155622096911221668,
%U 4201690015605193020,113442752267421552612,3062876603036110993314
%N Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A170747, 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="/A163548/b163548.txt">Table of n, a(n) for n = 0..695</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, -351).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
%F a(n) = 26*a(n-1)+26*a(n-2)+26*a(n-3)+26*a(n-4)-351*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)
%t coxG[{5,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 05 2018 *)
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6)) \\ _G. C. Greubel_, Jul 27 2017
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6) )); // _G. C. Greubel_, May 16 2019
%o (Sage) ((1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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