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%I #20 Sep 08 2022 08:45:43
%S 1,1,1,4,11,24,54,127,297,689,1600,3721,8652,20112,46753,108689,
%T 252673,587392,1365519,3174448,7379698,17155715,39882197,92714861,
%U 215535904,501060185,1164823608,2707886360,6295072049,14634267033,34020543361
%N Transform of A056594 by the T_{0,0} transformation (see link).
%H G. C. Greubel, <a href="/A159350/b159350.txt">Table of n, a(n) for n = 0..2700</a>
%H Richard Choulet, <a href="http://www.apmep.asso.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,4,-2,1).
%F O.g.f.: (1-z)^2/((1-3*z+2*z^2-z^3)*(1+z^2)).
%F 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)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11.
%p a(0):=1: a(1):=1: a(2):=1: a(3):=4: a(4):=11: 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 LinearRecurrence[{3,-3,4,-2,1}, {1,1,1,4,11}, 50] (* _G. C. Greubel_, Jun 15 2018 *)
%o (PARI) x='x+O('x^50); Vec((1-x)^2/((1-3*x+2*x^2-x^3)*(1+x^2))) \\ _G. C. Greubel_, Jun 15 2018
%o (Magma) I:=[1,1,1,4,11]; [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 15 2018
%Y Cf. A137531, A159347, A159348, A159349.
%K easy,nonn
%O 0,4
%A _Richard Choulet_, Apr 11 2009
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