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%I #40 Oct 07 2024 01:27:56
%S 1,3,12,51,216,915,3876,16419,69552,294627,1248060,5286867,22395528,
%T 94868979,401871444,1702354755,7211290464,30547516611,129401356908,
%U 548152944243,2322013133880,9836205479763,41666835052932,176503545691491,747681017818896,3167227616967075
%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
%H Stefano Spezia, <a href="/A155179/b155179.txt">Table of n, a(n) for n = 0..1500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,1).
%F G.f.: (1-x-x^2)/(1-4*x-x^2).
%F a(n) = Sum_{k=0..n} A155161(n,k)*3^k. - _Philippe Deléham_, Feb 08 2012
%F E.g.f.: 1 + 3*exp(2*x)*sinh(sqrt(5)*x)/sqrt(5). - _Stefano Spezia_, Oct 06 2024
%t 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
%Y Cf. A155161.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Jan 21 2009
%E Entries corrected by _Paolo P. Lava_, Jan 26 2009