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%I #15 Sep 08 2022 08:45:43
%S 1,1,1,4,11,24,56,129,300,698,1623,3773,8771,20390,47401,110194,
%T 256170,595523,1384423,3218393,7481856,17393205,40434296,93998334,
%U 218519615,507996473,1180948523,2745372238,6382216141,14836852470,34491497366
%N Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{0,0} transformation (see link).
%H G. C. Greubel, <a href="/A159349/b159349.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.: (1-2x+2x^3-2x^5+2x^6-2x^7+x^8)/(1-3x+2x^2-x^3). [corrected by _Georg Fischer_, May 19 2019]
%F a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n>=9, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11, a(5)=24, a(6)=56, a(7)=129, a(8)=300.
%p a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=11:a(5):=24:a(6):=56:a(7):=129:a(8):=300:for n from 6 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, 1, 4, 11, 24}, LinearRecurrence[{3, -2, 1}, {56, 129, 300}, 95]] (* _G. C. Greubel_, Jun 16 2018 *)
%o (PARI) m=50; v=concat([56,129,300], vector(m-3)); for(n=4, m, v[n]= 3*v[n-1] -2*v[n-2] +v[n-3]); concat([1,1,1,4,11,24], v) \\ _G. C. Greubel_, Jun 16 2018
%o (Magma) I:=[56, 129, 300]; [1,1,1,4,11,24] 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, A159347, A159348.
%K easy,nonn
%O 0,4
%A _Richard Choulet_, Apr 11 2009