%I #14 Sep 08 2022 08:45:43
%S 1,2,4,11,26,60,139,323,751,1746,4059,9436,21936,50995,118549,275593,
%T 640676,1489391,3462414,8049136,18711971,43500055,101125359,235087938,
%U 546513151,1270488936,2953528444,6866120611,15961793881,37106668865
%N Transform of the finite sequence (1, 0, -1) by the T_{1,0} transformation (see link).
%H G. C. Greubel, <a href="/A159336/b159336.txt">Table of n, a(n) for n = 0..1000</a>
%H Richard Choulet, <a href="http://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+(z/(1-3*z+2*z^2-z^3)).
%F a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 5, with a(0)=1, a(1)=2, a(2)=4, a(3)=11, a(4)=26.
%t Join[{1, 2}, LinearRecurrence[{3, -2, 1}, {4, 11, 26}, 49]] (* _G. C. Greubel_, Jun 25 2018 *)
%o (PARI) z='z+O('z^50); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+(z/(1-3*z+2*z^2-z^3))) \\ _G. C. Greubel_, Jun 25 2018
%o (Magma) I:=[4, 11, 26]; [1,2] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..50]]; // _G. C. Greubel_, Jun 25 2018
%Y Cf. A034943.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 11 2009