%I A005247 M0149
%S A005247 2,1,3,2,7,5,18,13,47,34,123,89,322,233,843,610,2207,1597,5778,4181,
%T A005247 15127,10946,39603,28657,103682,75025,271443,196418,710647,514229,
%U A005247 1860498,1346269,4870847,3524578,12752043,9227465,33385282,24157817
%N A005247 a(n) = 3a(n-2) - a(n-4), a(0)=2, a(1)=1, a(2)=3, a(3)=2. Alternates Lucas 
               (A000032) and Fibonacci (A000045) sequences for even and odd n.
%D A005247 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005247 T. Crilly, Double sequences of positive integers, Math. Gaz., 69 (1985), 
               263-271.
%H A005247 T. D. Noe, <a href="b005247.txt">Table of n, a(n) for n=0..500</a>
%H A005247 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005247 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A005247 a(0)=2, a(1)=1; a(2)=3, a(n)=(1+a(n-1)a(n-2))/a(n-3), n >= 3. a(-n)=a(n).
%F A005247 G.f.: (2+x-3*x^2-x^3)/((1-x-x^2)*(1+x-x^2))
%F A005247 a(n)=F(n) if n odd, a(n)=L(n) if n even. a(n)=F(n+1)+(-1)^nF(n-1). - 
               Mario Catalani (mario.catalani(AT)unito.it), Sep 20 2002
%p A005247 with(combinat): A005247 := n-> if n mod 2 = 1 then fibonacci(n) else 
               fibonacci(n+1)+fibonacci(n-1); fi;
%p A005247 A005247:=-(z+1)*(3*z**2-z-1)/(z**2-z-1)/(z**2+z-1); [S. Plouffe in his 
               1992 dissertation. Gives sequence with an additional leading 1.]
%t A005247 CoefficientList[Series[(2 + x - 3x^2 - x^3)/(1 - 3x^2 + x^4), {x, 0, 
               40}], x]
%o A005247 (PARI) a(n)=if(n%2,fibonacci(n),fibonacci(n+1)+fibonacci(n-1))
%Y A005247 Cf. A000032, A000045, A005013, A005013.
%Y A005247 Sequence in context: A144238 A082833 A101709 this_sequence A135259 A122147 
               A141486
%Y A005247 Adjacent sequences: A005244 A005245 A005246 this_sequence A005248 A005249 
               A005250
%K A005247 nonn,nice,easy
%O A005247 0,1
%A A005247 N. J. A. Sloane (njas(AT)research.att.com).
%E A005247 Additional comments from Michael Somos, May 01 2000