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A163748 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163748 #19 Sep 08 2022 08:45:47
%S A163748 1,44,1892,81356,3498308,150426298,6468290136,278134727640,
%T A163748 11959718115576,514264646533176,22113240807047082,950863378003793100,
%U A163748 40886868257711476308,1758124284303633320844,75598869044590717310100
%N A163748 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163748 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A163748 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163748 G. C. Greubel, <a href="/A163748/b163748.txt">Table of n, a(n) for n = 0..610</a>
%H A163748 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (42,42,42,42,-903).
%F A163748 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%F A163748 a(n) = 42*a(n-1)+42*a(n-2)+42*a(n-3)+42*a(n-4)-903*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%p A163748 seq(coeff(series((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Aug 09 2019
%t A163748 CoefficientList[Series[(1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 02 2017 *)
%t A163748 coxG[{5, 903, -42}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 09 2019 *)
%o A163748 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6)) \\ _G. C. Greubel_, Aug 02 2017
%o A163748 (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 A163748 (Sage)
%o A163748 def A163748_list(prec):
%o A163748     P.<t> = PowerSeriesRing(ZZ, prec)
%o A163748     return P((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6)).list()
%o A163748 A163748_list(20) # _G. C. Greubel_, Aug 09 2019
%o A163748 (GAP) a:=[44, 1892, 81356, 3498308, 150426298];; for n in [6..30] do a[n]:=42*(a[n-1]+a[n-2]+a[n-3] +a[n-4]) -903*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 09 2019
%K A163748 nonn
%O A163748 0,2
%A A163748 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009