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A163745 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163745 #16 Sep 08 2022 08:45:47
%S A163745 1,43,1806,75852,3185784,133802025,5619647124,236023587219,
%T A163745 9912923799660,416339991317124,17486161688852682,734413837213650321,
%U A163745 30845173108213815708,1295488532304021561975,54410151353124129064362
%N A163745 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163745 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A163745 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163745 G. C. Greubel, <a href="/A163745/b163745.txt">Table of n, a(n) for n = 0..614</a>
%H A163745 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, -861).
%F A163745 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%F A163745 a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)+41*a(n-4)-861*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%p A163745 seq(coeff(series((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Aug 09 2019
%t A163745 CoefficientList[Series[(1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 02 2017 *)
%t A163745 coxG[{5, 865, -41}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 09 2019 *)
%o A163745 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6)) \\ _G. C. Greubel_, Aug 02 2017
%o A163745 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6) )); // _G. C. Greubel_, Aug 09 2019
%o A163745 (Sage)
%o A163745 def A163745_list(prec):
%o A163745     P.<t> = PowerSeriesRing(ZZ, prec)
%o A163745     return P((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6)).list()
%o A163745 A163745_list(20) # _G. C. Greubel_, Aug 09 2019
%K A163745 nonn
%O A163745 0,2
%A A163745 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009