%I A128588
%S A128588 1,2,4,6,10,16,26,42,68,110,178,288,466,754,1220,1974,3194,5168,8362,
%T A128588 13530,21892,35422,57314,92736,150050,242786,392836,635622,1028458,
%U A128588 1664080
%N A128588 A007318 * A128587.
%C A128588 a(n)/a(n-1) tends to phi, 1.618...
%C A128588 From A014217=1,1,2,4,6,. Which leads to A153819=16,34,88,. Inverse binomial 
               transform of A069403=1,3,9,25,67. [From Paul Curtz (bpcrtz(AT)free.fr), 
               Jan 03 2009]
%C A128588 Variation on "Narayana's Cows". One cow at step n=1. At any subsequent 
               step any cow generates another one but after two steps dies. The 
               sequence gives the total number of cows at any steps. [From Paolo 
               P. Lava (ppl(AT)spl.at), Oct 07 2009]
%H A128588 B. Winterfjord, <a href="http://www.math.chalmers.se/~einar/exjobb/winterfjord.pdf">
               Binary strings and substring avoidance</a>.
%H A128588 J.-P. Allouche and T. Johnson, <a href="http://www.lri.fr/~allouche/johnson2.pdf"> 
               Narayana's Cows and Delayed Morphisms</a>. [From Paolo P. Lava (ppl(AT)spl.at), 
               Oct 07 2009]
%F A128588 Binomial transform of A128587; a(n+2) = a(n+1) + a(n), n>3.
%F A128588 Apart from the initial term, double the Fibonacci numbers. O.g.f.: x*(1+x+x^2)/
               (1-x-x^2). a(n) gives the number of binary strings of length n-1 
               avoiding the substrings 000 and 111. a(n) also gives the number of 
               binary strings of length n-1 avoiding the substrings 010 and 101. 
               - Peter Bala (pbala(AT)toucansurf.com), Jan 22 2008
%F A128588 a(n)=A068922(n-1), n>2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 14 2008
%e A128588 a(4) = 6 = 1*1 + 3*1 + 3*1 + 1*(-1); where A128587 = (1, 1, 1, -1, 3, 
               -5, 9,...).
%Y A128588 Cf. A128587, A128586, A007318.
%Y A128588 Cf. A006355, A055389.
%Y A128588 Sequence in context: A028488 A080432 A094985 this_sequence A023613 A065795 
               A000801
%Y A128588 Adjacent sequences: A128585 A128586 A128587 this_sequence A128589 A128590 
               A128591
%K A128588 nonn
%O A128588 1,2
%A A128588 Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 11 2007
%E A128588 More terms from Peter Bala (pbala(AT)toucansurf.com), Jan 22 2008