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%I #11 Sep 08 2022 08:45:43
%S 2,4,9,23,55,126,292,679,1579,3671,8534,19839,46120,107216,249247,
%T 579429,1347009,3131416,7279659,16923154,39341560,91458031,212614127,
%U 494267879,1149033414,2671178611,6209736884,14435886844,33559365375
%N Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,1} transformation (see link).
%H G. C. Greubel, <a href="/A159330/b159330.txt">Table of n, a(n) for n = 0..1000</a>
%H R. Choulet, <a href="http://www.apmep.asso.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^4)+(z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3).
%F a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 7, with a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=55, a(5)=126, a(6)=292.
%t Join[{2, 4, 9, 23}, LinearRecurrence[{3, -2, 1}, {55, 126, 292}, 47]] (* _G. C. Greubel_, Jun 26 2018 *)
%o (PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4)+(z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ _G. C. Greubel_, Jun 26 2018
%o (Magma) I:=[55, 126, 292]; [2, 4, 9, 23] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..30]]; // _G. C. Greubel_, Jun 26 2018
%Y Cf. A159328, A159329.
%K easy,nonn
%O 0,1
%A _Richard Choulet_, Apr 10 2009
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