cp's OEIS Frontend

A159340 Transform of the finite sequence (1, 0, -1) by the T_{0,1} transformation (see link).

%I A159340 #13 Sep 08 2022 08:45:43
%S A159340 2,3,6,16,38,88,204,474,1102,2562,5956,13846,32188,74828,173954,
%T A159340 404394,940102,2185472,5080606,11810976,27457188,63830218,148387254,
%U A159340 344958514,801931252,1864263982,4333887956,10075067156,23421689538,54448822258
%N A159340 Transform of the finite sequence (1, 0, -1) by the T_{0,1} transformation (see link).
%H A159340 G. C. Greubel, <a href="/A159340/b159340.txt">Table of n, a(n) for n = 0..1000</a>
%H A159340 Richard Choulet, <a href="http://www.apmep.asso.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A159340 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F A159340 O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+((1-z+z^2)/(1-3*z+2*z^2-z^3)).
%F A159340 a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 5, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=38.
%p A159340 a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=38:for n from 2 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
%t A159340 Join[{2, 3}, LinearRecurrence[{3, -2, 1}, {6, 16, 38}, 49]] (* _G. C. Greubel_, Jun 25 2018 *)
%o A159340 (PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ _G. C. Greubel_, Jun 25 2018
%o A159340 (Magma) I:=[6, 16, 38]; [2, 3] 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 A159340 Cf. A135364.
%K A159340 easy,nonn
%O A159340 0,1
%A A159340 _Richard Choulet_, Apr 11 2009