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%I #22 Jan 03 2024 08:47:37
%S 1,3,12,51,216,915,3876,16419,69552,294627,1248060,5286867,22395528,
%T 94868979,401871444,1702354755,7211290464,30547516611,129401356908,
%U 548152944243,2322013133880,9836205479763,41666835052932
%N a(n)=4*a(n-1)+a(n-2), n>2; a(0)=1, a(1)=3, a(2)=12.
%C For n > 0, integers in 3/2 * the Fibonacci sequence. - _Vladimir Joseph Stephan Orlovsky_, Oct 25 2009
%F G.f.: (1-x-x^2)/((1-4*x-x^2).
%F a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*3^k. - _Philippe Deléham_, Feb 08 2012
%t Clear[f,lst,n,a] f[n_]:=Fibonacci[n]; lst={};Do[a=f[n]*(3/2);If[IntegerQ[a],AppendTo[lst,a]],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 25 2009 *)
%o (PARI) Vec((1-x-x^2)/((1-4*x-x^2)+O(x^99))) \\ _Charles R Greathouse IV_, Dec 09 2014
%o (PARI) concat(1,select(n->denominator(n)==1,[fibonacci(n)*3/2|n<-[1..50]])) \\ _Charles R Greathouse IV_, Dec 09 2014
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Jan 21 2009
%E Entries corrected by _Paolo P. Lava_, Jan 26 2009
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