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A159338 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{1,0} transformation (see link).

%I A159338 #13 Sep 08 2022 08:45:43
%S A159338 1,2,4,11,27,61,140,327,761,1769,4112,9559,22222,51660,120095,279187,
%T A159338 649031,1508814,3507567,8154104,18955992,44067335,102444125,238153697,
%U A159338 553640176,1287057259,2992045122,6955661024,16169950087,37590573335
%N A159338 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{1,0} transformation (see link).
%H A159338 G. C. Greubel, <a href="/A159338/b159338.txt">Table of n, a(n) for n = 0..1000</a>
%H A159338 Richard Choulet, <a href="http://www.apmep.asso.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A159338 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F A159338 O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4-z^6)+(z/(1-3*z+2*z^2-z^3)).
%F A159338 a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 9, with a(0)=1, a(1)=2, a(2)=4, a(3)=11, a(4)=27, a(5)=61, a(6)=140, a(7)=327, a(8)=761.
%p A159338 a(0):=1: a(1):=2:a(2):=4: a(3):=11:a(4):=27:a(5):=61:a(6):=140:a(7):=327:a(8):=761:for n from 6 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
%t A159338 Join[{1, 2, 4, 11, 27, 61}, LinearRecurrence[{3, -2, 1}, {140, 327, 761}, 45]] (* _G. C. Greubel_, Jun 25 2018 *)
%o A159338 (PARI) z='z+O('z^50); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4-z^6)+(z/(1-3*z+2*z^2-z^3))) \\ _G. C. Greubel_, Jun 25 2018
%o A159338 (Magma) I:=[140, 327, 761]; [1, 2, 4, 11, 27, 61] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..50]]; // _G. C. Greubel_, Jun 25 2018
%Y A159338 Cf. A034943, A159336, A159337.
%K A159338 easy,nonn
%O A159338 0,2
%A A159338 _Richard Choulet_, Apr 11 2009