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A159329 Transform of the finite sequence (1, 0, -1) by the T_{1,1} transformation (see link).

%I A159329 #12 Sep 08 2022 08:45:43
%S A159329 2,4,9,23,54,125,290,674,1567,3643,8469,19688,45769,106400,247350,
%T A159329 575019,1336757,3107583,7224254,16794353,39042134,90761950,210995935,
%U A159329 490506039,1140288197,2650848448,6162474989,14326016268,33303947274
%N A159329 Transform of the finite sequence (1, 0, -1) by the T_{1,1} transformation (see link).
%H A159329 G. C. Greubel, <a href="/A159329/b159329.txt">Table of n, a(n) for n = 0..1000</a>
%H A159329 Richard Choulet <a href="http://www.apmep.asso.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation </a>
%H A159329 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F A159329 O.g.f.: 2+4*x -x^2*(9-4*x+3*x^2) / ( -1+3*x-2*x^2+x^3 ).
%F A159329 a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=54 and for n>=2 a(n+3)=3*a(n+2)-2*a(n+1)+a(n).
%t A159329 Join[{2,4}, LinearRecurrence[{3, -2, 1}, {9, 23, 54}, 50]] (* _G. C. Greubel_, Jun 26 2018 *)
%o A159329 (PARI) x='x+O('x^30); Vec(2+4*x -x^2*(9-4*x+3*x^2)/(-1+3*x-2*x^2+x^3)) \\ _G. C. Greubel_, Jun 26 2018
%o A159329 (Magma) I:=[9, 23, 54]; [2,4] 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 A159329 Cf. A159328.
%K A159329 easy,nonn
%O A159329 0,1
%A A159329 _Richard Choulet_, Apr 10 2009