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A163440 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163440 #15 Sep 08 2022 08:45:46
%S A163440 1,15,210,2940,41160,576135,8064420,112881405,1580053020,22116729180,
%T A163440 309578036040,4333306233165,60655281460410,849019887139515,
%U A163440 11884122064943310,166347525415813560,2328442863574420320
%N A163440 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163440 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A163440 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163440 G. C. Greubel, <a href="/A163440/b163440.txt">Table of n, a(n) for n = 0..855</a>
%H A163440 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, -91).
%F A163440 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
%F A163440 a(n) = 13*a(n-1)+13*a(n-2)+13*a(n-3)+13*a(n-4)-91*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163440 CoefficientList[Series[(1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, 13, 13, 13, -91}, {15, 210, 2940, 41160, 576135}, 30] (* _G. C. Greubel_, Dec 23 2016 *)
%t A163440 coxG[{5, 91, -13}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 12 2019 *)
%o A163440 (PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)) \\ _G. C. Greubel_, Dec 23 2016
%o A163440 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6) )); // _G. C. Greubel_, May 12 2019
%o A163440 (Sage) ((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 12 2019
%K A163440 nonn
%O A163440 0,2
%A A163440 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009