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A159343 Transform of A056594 by the T_{0,1} transformation (see link).

%I A159343 #13 Sep 08 2022 08:45:43
%S A159343 2,3,6,16,39,89,205,478,1113,2586,6010,13973,32485,75517,175554,
%T A159343 408115,948754,2205584,5127359,11919665,27709861,64417610,149752773,
%U A159343 348132962,809310950,1881419697,4373770153,10167782017,23637225442,54949882443
%N A159343 Transform of A056594 by the T_{0,1} transformation (see link).
%H A159343 G. C. Greubel, <a href="/A159343/b159343.txt">Table of n, a(n) for n = 0..2500</a>
%H A159343 Richard Choulet, <a href="http://www.apmep.asso.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A159343 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,4,-2,1).
%F A159343 O.g.f.: ((1-z)^2/(1-3*z+2*z^2-z^3))*(1/(1+z^2))+((1-z+z^2)/(1-3*z+2*z^2-z^3)).
%F A159343 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)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=39.
%p A159343 a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39: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 A159343 LinearRecurrence[{3, -3, 4, -2, 1}, {2, 3, 6, 16, 39}, 50] (* _G. C. Greubel_, Jun 17 2018 *)
%o A159343 (PARI) m=32; v=concat([2, 3, 6, 16, 39], vector(m-5)); for(n=6, m, v[n] = 3*v[n-1] -3*v[n-2] +4*v[n-3] -2*v[n-4] +v[n-5]); v \\ _G. C. Greubel_, Jun 17 2018
%o A159343 (Magma) I:=[2, 3, 6, 16, 39]; [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 17 2018
%Y A159343 Cf. A135364, A159340, A159441, A159442.
%K A159343 easy,nonn
%O A159343 0,1
%A A159343 _Richard Choulet_, Apr 11 2009