cp's OEIS Frontend

A159341 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,1} transformation (see link).

%I A159341 #16 Sep 08 2022 08:45:43
%S A159341 2,3,6,16,39,89,206,479,1114,2590,6021,13997,32539,75644,175851,
%T A159341 408804,950354,2209305,5136011,11939777,27756614,64526299,150005446,
%U A159341 348720354,810676469,1884594145,4381149851,10184937732,23677107639,55042597304
%N A159341 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,1} transformation (see link).
%H A159341 G. C. Greubel, <a href="/A159341/b159341.txt">Table of n, a(n) for n = 0..1000</a>
%H A159341 Richard Choulet, <a href="http://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A159341 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F A159341 O.g.f: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4) + ((1-z+z^2)/(1-3*z+2*z^2-z^3)).
%F A159341 a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 7, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=39, a(5)=89, a(6)=206.
%p A159341 a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:a(5):=89:a(6):=206:for n from 4 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
%t A159341 Join[{2, 3, 6, 16}, LinearRecurrence[{3, -2, 1}, {39, 89, 206}, 47]] (* _G. C. Greubel_, Jun 25 2018 *)
%o A159341 (PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ _G. C. Greubel_, Jun 25 2018
%o A159341 (Magma) I:=[39, 89, 206]; [2, 3, 6, 16] cat [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 25 2018
%Y A159341 Cf. A135364, A159340.
%K A159341 easy,nonn
%O A159341 0,1
%A A159341 _Richard Choulet_, Apr 11 2009