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A163226 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%I A163226 #15 Sep 08 2022 08:45:46
%S A163226 1,43,1806,75852,3184881,133727076,5614945203,235760834988,
%T A163226 9899147615406,415646320207041,17452195907135052,732784406294332791,
%U A163226 30768219023291805678,1291898809163525952060,54244365975641552431917
%N A163226 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163226 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A163226 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163226 G. C. Greubel, <a href="/A163226/b163226.txt">Table of n, a(n) for n = 0..610</a>
%H A163226 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, -861).
%F A163226 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%F A163226 a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)-861*a(n-4). - _Wesley Ivan Hurt_, May 06 2021
%t A163226 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(861*t^4-41*t^3-41*t^2 - 41*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {41, 41, 41, -861}, {43,1806,75852,3184881}, 20]] (* _G. C. Greubel_, Dec 11 2016 *)
%t A163226 coxG[{4, *61, -41}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 30 2019 *)
%o A163226 (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(861*t^4-41*t^3 - 41*t^2-41*t+1)) \\ _G. C. Greubel_, Dec 11 2016
%o A163226 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-42*x+902*x^4-861*x^5) )); // _G. C. Greubel_, Apr 30 2019
%o A163226 (Sage) ((1+x)*(1-x^4)/(1-42*x+902*x^4-861*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 30 2019
%K A163226 nonn
%O A163226 0,2
%A A163226 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009