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A179134 a(n) = (F(2*n-1) + F(2*n+2)) * (5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).

%I A179134 #10 Oct 18 2020 15:48:12
%S A179134 1,4,10,13,68,178,233,1220,3194,4181,21892,57314,75025,392836,1028458,
%T A179134 1346269,7049156,18454930,24157817,126491972,331160282,433494437,
%U A179134 2269806340,5942430146,7778742049,40730022148,106632582346
%N A179134 a(n) = (F(2*n-1) + F(2*n+2)) * (5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).
%H A179134 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,18,0,0,-1).
%F A179134 a(n) = 18*a(n-3)-a(n-6). G.f.: -(2*x^5+4*x^4+5*x^3-10*x^2-4*x-1) / ((x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). - _Colin Barker_, Jun 27 2013
%p A179134 with(combinat): nmax:=28; for n from 0 to nmax do a(n):=(fibonacci(2*n-1)+fibonacci(2*n+2))*(5/6-cos(2*Pi*n/3)/3) od: seq(a(n),n=0..nmax);
%Y A179134 Cf. A128052, A000045 (Fibonacci numbers).
%Y A179134 Appears in A179133.
%K A179134 easy,nonn
%O A179134 0,2
%A A179134 _Johannes W. Meijer_, Jul 01 2010