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A163749 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163749 #22 Sep 08 2022 08:45:47
%S A163749 1,45,1980,87120,3833280,168663330,7421142960,326528374590,
%T A163749 14367164193360,632151515809440,27814503513864870,1223830974655177020,
%U A163749 53848246968666559530,2369308966391783748420,104248982914726676312880
%N A163749 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163749 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A163749 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163749 G. C. Greubel, <a href="/A163749/b163749.txt">Table of n, a(n) for n = 0..605</a>
%H A163749 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (43,43,43,43,-946).
%F A163749 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%F A163749 a(n) = 43*a(n-1)+43*a(n-2)+43*a(n-3)+43*a(n-4)-946*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%p A163749 seq(coeff(series((1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Aug 09 2019
%t A163749 CoefficientList[Series[(1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 02 2017 *)
%t A163749 coxG[{5, 946, -43}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 09 2019 *)
%o A163749 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6)) \\ _G. C. Greubel_, Aug 02 2017
%o A163749 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6) )); // _G. C. Greubel_, Aug 09 2019
%o A163749 (Sage)
%o A163749 def A163749_list(prec):
%o A163749     P.<t> = PowerSeriesRing(ZZ, prec)
%o A163749     return P((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6)).list()
%o A163749 A163749_list(20) # _G. C. Greubel_, Aug 09 2019
%o A163749 (GAP) a:=[45, 1980, 87120, 3833280, 168663330];; for n in [6..30] do a[n]:=43*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -946*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 09 2019
%K A163749 nonn
%O A163749 0,2
%A A163749 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009