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%I #26 Sep 08 2022 08:45:18
%S 2,2,-2,-12,-22,-10,56,174,222,-92,-1038,-2210,-1624,4102,16006,24260,
%T 954,-86426,-215528,-212546,267150,1433124,2538530,984270,-6873592,
%U -20465066,-25058698,13402052,124569514,256580886,173699192,-512667826,-1893337666
%N a(n) = a(n-1) - 2*a(n-2) - 3*a(n-3) - ... - (n-1)*a(1), with a(1) = a(2) = 2, a(3) = -2.
%H G. C. Greubel, <a href="/A106541/b106541.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-5,2).
%F a(n) = a(n-1) - Sum_{k=2..n-1} k*a(n-k), with a(1) = a(2) = 2, a(3) = -2.
%F a(n) = 2*A106540(n).
%F From _Colin Barker_, Aug 25 2016: (Start)
%F a(n) = 3*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.
%F G.f.: 2*x*(1-x)^2/(1-3*x+5*x^2-2*x^3). (End)
%t lst={2,2,-2};f[n_]:=With[{c=(Times@@@Thread[{lst,Range[Length[lst],1, -1]}])}, Last[c]- Total[Most[c]]]; Do[AppendTo[lst,f[lst]],{40}];lst (* _Harvey P. Dale_, Apr 17 2012 *)
%o (Magma) I:=[2,2,-2]; [n le 3 select I[n] else 3*Self(n-1) - 5*Self(n-2) + 2*Self(n-3): n in [1..41]]; // _G. C. Greubel_, Sep 03 2021
%o (Sage)
%o def A106541_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 2*x*(1-x)^2/(1-3*x+5*x^2-2*x^3) ).list()
%o a=A106541_list(41); a[1:] # _G. C. Greubel_, Sep 03 2021
%Y Cf. A106540, A106542.
%K easy,sign
%O 1,1
%A _Alexandre Wajnberg_, May 08 2005
%E More terms from _Harvey P. Dale_, Apr 17 2012
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