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A159328 Transform of 1 by the T_{1,1} transformation (see link).

%I A159328 #13 Jun 02 2025 01:31:28
%S A159328 2,4,10,24,56,130,302,702,1632,3794,8820,20504,47666,110810,257602,
%T A159328 598852,1392162,3236384,7523680,17490434,40660326,94523790,219741152,
%U A159328 510836202,1187550092,2760719024,6417893090,14919791314,34684306786
%N A159328 Transform of 1 by the T_{1,1} transformation (see link).
%H A159328 G. C. Greubel, <a href="/A159328/b159328.txt">Table of n, a(n) for n = 0..1000</a>
%H A159328 Richard Choulet <a href="http://www.apmep.asso.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation </a>
%H A159328 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F A159328 O.g.f f(z)=((1-z)^2/(1-3*z+2*z^2-z^3))*1+(z/(1-3*z+2*z^2-z^3))+((1-z+z^2)/(1-3*z+2*z^2-z^3)).
%F A159328 a(0), a(1)=4, a(2)=10 and for n>=0 a(n+3)=3*a(n+2)-2*a(n+1)+a(n).
%F A159328 a(n) = 2*A034943(n+2). - _R. J. Mathar_, Feb 19 2016
%t A159328 LinearRecurrence[{3,-2,1},{2,4,10},30] (* _Harvey P. Dale_, May 10 2016 *)
%o A159328 (PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*1+(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 A159328 (Magma) I:=[2,4,10]; [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 A159328 Cf. A034943.
%K A159328 easy,nonn
%O A159328 0,1
%A A159328 _Richard Choulet_, Apr 10 2009