1,2

a(n)/a(n-1) tends to phi, 1.618...

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]

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]

B. Winterfjord, Binary strings and substring avoidance.

J.-P. Allouche and T. Johnson, Narayana's Cows and Delayed Morphisms. [From Paolo P. Lava (ppl(AT)spl.at), Oct 07 2009]

Binomial transform of A128587; a(n+2) = a(n+1) + a(n), n>3.

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

a(n)=A068922(n-1), n>2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 14 2008

a(4) = 6 = 1*1 + 3*1 + 3*1 + 1*(-1); where A128587 = (1, 1, 1, -1, 3, -5, 9,...).

Cf. A128587, A128586, A007318.

Cf. A006355, A055389.

Sequence in context: A028488 A080432 A094985 this_sequence A023613 A065795 A000801

Adjacent sequences: A128585 A128586 A128587 this_sequence A128589 A128590 A128591

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 11 2007

More terms from Peter Bala (pbala(AT)toucansurf.com), Jan 22 2008