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A159339 Transform of A056594 by the T_{1,0} transformation (see link).

%I A159339 #19 Sep 08 2022 08:45:43
%S A159339 1,2,4,11,27,61,140,327,762,1770,4113,9563,22233,51684,120149,279314,
%T A159339 649328,1509503,3509167,8157825,18964644,44087447,102490878,238262386,
%U A159339 553892849,1287644651,2993410641,6958835472,16177329785,37607729050
%N A159339 Transform of A056594 by the T_{1,0} transformation (see link).
%H A159339 G. C. Greubel, <a href="/A159339/b159339.txt">Table of n, a(n) for n = 0..1000</a>
%H A159339 Richard Choulet, <a href="http://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A159339 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,4,-2,1).
%F A159339 O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1/(1+z^2))+(z/(1-3*z+2*z^2-z^3)).
%F A159339 a(n) = 3*a(n-1) - 3*a(n-2) + 4*a(n-3) - 2*a(n-4) + a(n-5) for n >= 5, with a(0)=1, a(1)=2, a(2)=4, a(3)=11, a(4)=27.
%p A159339 a(0):=1: a(1):=2:a(2):=4: a(3):=11:a(4):=27:for n from 0 to 31 do a(n+5):=3*a(n+4)-3*a(n+3)+4*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
%t A159339 LinearRecurrence[{3, -3, 4, -2, 1}, {1, 2, 4, 11, 27}, 50] (* _G. C. Greubel_, Jun 25 2018 *)
%o A159339 (PARI) z='z+O('z^50); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1/(1+z^2))+(z/(1-3*z+2*z^2-z^3))) \\ _G. C. Greubel_, Jun 25 2018
%o A159339 (Magma) I:=[1, 2, 4, 11, 27]; [n le 5 select I[n] else 3*Self(n-1) - 3*Self(n-2) + 4*Self(n-3) -2*Self(n-4) +Self(n-5): n in [1..50]]; // _G. C. Greubel_, Jun 25 2018
%Y A159339 Cf. A034943, A159336, A159337, A159338.
%K A159339 easy,nonn
%O A159339 0,2
%A A159339 _Richard Choulet_, Apr 11 2009