cp's OEIS Frontend

A159337 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,0} transformation (see link).

%I A159337 #13 Sep 08 2022 08:45:43
%S A159337 1,2,4,11,27,61,141,328,763,1774,4124,9587,22287,51811,120446,280003,
%T A159337 650928,1513224,3517819,8177937,19011397,44196136,102743551,238849778,
%U A159337 555258368,1290819099,3000790339,6975991187,16217211982,37700443911
%N A159337 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,0} transformation (see link).
%H A159337 G. C. Greubel, <a href="/A159337/b159337.txt">Table of n, a(n) for n = 0..1000</a>
%H A159337 Richard Choulet, <a href="http://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A159337 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F A159337 O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4)+(z/(1-3*z+2*z^2-z^3)).
%F A159337 a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 7, with a(0)=1, a(1)=2,a(2)=4, a(3)=11, a(4)=27, a(5)=61, a(6)=141.
%p A159337 a(0):=1: a(1):=2:a(2):=4: a(3):=11:a(4):=27:a(5):=61:a(6):=141: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 A159337 Join[{1, 2, 4, 11}, LinearRecurrence[{3, -2, 1}, {27, 61, 141}, 997]] (* _G. C. Greubel_, Jun 25 2018 *)
%o A159337 (PARI) z='z+O('z^50); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4)+(z/(1-3*z+2*z^2-z^3))) \\ _G. C. Greubel_, Jun 25 2018
%o A159337 (Magma) I:=[27, 61, 141]; [1, 2, 4, 11] 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 A159337 Cf. A159336.
%K A159337 easy,nonn
%O A159337 0,2
%A A159337 _Richard Choulet_, Apr 11 2009