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%I #15 Sep 08 2022 08:45:43
%S 1,1,1,4,10,23,53,123,286,665,1546,3594,8355,19423,45153,104968,
%T 244021,567280,1318766,3065759,7127025,16568323,38516678,89540413,
%U 208156206,483904470,1124941411,2615171499,6079536145,14133206848,32855719753
%N Transform of the finite sequence (1, 0, -1) by the T_{0,0} transformation.
%C Without the first two 1's: A137531.
%H G. C. Greubel, <a href="/A159347/b159347.txt">Table of n, a(n) for n = 0..2500</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_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F O.g.f.: f(z) = ((1-z)^2/(1 - 3*z + 2*z^2 - z^3))*(1-z^2).
%F a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 5, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=10.
%F a(n) = A137531(n-2).
%p a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=10: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 Join[{1,1}, LinearRecurrence[{3,-2,1}, {1,4,10}, 50]] (* _G. C. Greubel_, Jun 16 2018 *)
%o (PARI) m=50; v=concat([1,4,10], vector(m-3)); for(n=4, m, v[n] = 3*v[n-1] -2*v[n-2] +v[n-3] ); concat([1,1], v) \\ _G. C. Greubel_, Jun 16 2018
%o (Magma) I:=[1,4,10]; [1,1] 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 16 2018
%Y Cf. A137531.
%K easy,nonn
%O 0,4
%A _Richard Choulet_, Apr 11 2009
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