%I A005672 M3253
%S A005672 0,0,0,1,1,4,5,13,18,39,57,112,169,313,482,859,1341,2328,3669,6253,9922,
%T A005672 16687,26609,44320,70929,117297,188226,309619,497845,815656,1313501,2145541
%N A005672 Fibonacci(n+1)-2^[n/2].
%D A005672 R. K. Guy, personal communication.
%D A005672 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005672 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 A005672 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 A005672 a(n) =Fibonacci(n-1)+2*a(n-2), a(-1)=0, a(1)=0, a(2)=1. - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 17 2008
%p A005672 A005672:=z**3/(z**2+z-1)/(-1+2*z**2); [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%p A005672 with (combinat):a[ -1]:=0:a[1]:=0:a[2]:=1:for n from 2 to 50 do a[n]:=fibonacci(n-1)+2*a[n-2] 
               od: seq(a[n-1], n=0..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 17 2008
%Y A005672 Gives diagonal sums of triangle A054143.
%Y A005672 Sequence in context: A083709 A091183 A094029 this_sequence A147001 A140683 
               A071341
%Y A005672 Adjacent sequences: A005669 A005670 A005671 this_sequence A005673 A005674 
               A005675
%K A005672 nonn,easy
%O A005672 0,6
%A A005672 N. J. A. Sloane (njas(AT)research.att.com).