%I A005673 M1578
%S A005673 0,0,0,0,1,2,6,11,24,42,81,138,250,419,732,1214,2073,3414,5742,9411,
%T A005673 15664,25586,42273,68882,113202,184131,301428,489654,799273,1297118,2112774
%N A005673 F(n+1)-2^[ (n+1)/2 ] -2^[ n/2 ] +1.
%D A005673 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005673 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A005673 R. K. Guy, personal communication.
%H A005673 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 A005673 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 A005673 G.f. : x^4/((1-x)(1-x-x^2)(1-2x^2)); a(n)=2a(n-1)+2a(n-2)-5a(n-3)+2a(n-4); 
               a(n+1)=sum{k=0..n, (2^floor(k/2)-1)F(n-k)}. - Paul Barry (pbarry(AT)wit.ie), 
               Jul 28 2004
%p A005673 A005673:=-z**4/(z-1)/(z**2+z-1)/(-1+2*z**2); [Conjectured by S. Plouffe 
               in his 1992 dissertation.]
%Y A005673 Sequence in context: A102429 A080012 A103143 this_sequence A084308 A067605 
               A072986
%Y A005673 Adjacent sequences: A005670 A005671 A005672 this_sequence A005674 A005675 
               A005676
%K A005673 nonn
%O A005673 0,6
%A A005673 N. J. A. Sloane (njas(AT)research.att.com).