%I #11 Sep 08 2022 08:45:43
%S 2,4,10,24,56,130,302,702,1632,3794,8820,20504,47666,110810,257602,
%T 598852,1392162,3236384,7523680,17490434,40660326,94523790,219741152,
%U 510836202,1187550092,2760719024,6417893090,14919791314,34684306786
%N Transform of 1 by the T_{1,1} transformation (see link)
%H G. C. Greubel, <a href="/A159328/b159328.txt">Table of n, a(n) for n = 0..1000</a>
%H Richard 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/(1-3*z+2*z^2-z^3))+((1-z+z^2)/(1-3*z+2*z^2-z^3)).
%F 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 a(n) = 2*A034943(n+2). - _R. J. Mathar_, Feb 19 2016
%t LinearRecurrence[{3,-2,1},{2,4,10},30] (* _Harvey P. Dale_, May 10 2016 *)
%o (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 (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 Cf. A034943.
%K easy,nonn
%O 0,1
%A _Richard Choulet_, Apr 10 2009