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 A281185 a(0)=0, a(1)=1, a(2)=0; thereafter, a(2n)=a(n)+a(n+1) for n >= 2, a(2n+1)=a(n) for n >= 1. 2
 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 2, 0, 3, 2, 2, 1, 2, 1, 3, 1, 2, 2, 3, 0, 5, 3, 4, 2, 3, 2, 3, 1, 3, 2, 4, 1, 4, 3, 3, 1, 4, 2, 5, 2, 3, 3, 5, 0, 8, 5, 7, 3, 6, 4, 5, 2, 5, 3, 5, 2, 4, 3, 4, 1, 5, 3, 6, 2, 5, 4, 5, 1, 7, 4, 6, 3, 4, 3, 5, 1, 6, 4, 7, 2, 7, 5, 5, 2, 6, 3, 8, 3, 5, 5, 8, 0, 13, 8, 12, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS A "bow" sequence. The bow sequences are a family of recursive sequences defined to have the flipped recursion from the Stern sequence A002487 (called bow for the opposite end of the boat from the stern).  The bow sequences require two initial conditions: a(1)=alpha, a(2)=beta. We also define a(0)=0, although it does not enter into the recursion. The bow sequences then follow the recursion a(2n)=a(n)+a(n+1) for n at least 2, and a(2n+1)=a(n).  This particular bow sequence has initial conditions a(1)=0, a(2)=1 and (along with the sequence A106345 with initial conditions a(1)=1, a(2)=0) is of particular importance when studying the general bow sequences. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..25000 M. Dennison, A Sequence Related to the Stern Sequence, Ph.D. dissertation, University of Illinois at Urbana-Champaign, 2010. Melissa Dennison, On Properties of the General Bow Sequence, J. Int. Seq., Vol. 22 (2019), Article 19.2.7. EXAMPLE a(3)=a(1)=1, a(4)=a(2)+a(3)=0+1=1, a(5)=a(2)=0. MAPLE f:=proc(n) option remember; if n=0 then 0 elif n=1 then 1 elif n=2 then 0 else    if n mod 2 = 0 then f(n/2)+f(1+n/2) else f((n-1)/2) fi; fi; end; [seq(f(n), n=0..150)]; # N. J. A. Sloane, Apr 26 2017 MATHEMATICA b=0; b=1; b=0; b[n_?EvenQ]:=b[n]=b[n/2]+b[n/2+1]; b[n_?OddQ]:=b[n]=b[(n-1)/2] CROSSREFS Cf. A002487, A106345. Sequence in context: A035180 A163819 A301734 * A260683 A092673 A243842 Adjacent sequences:  A281182 A281183 A281184 * A281186 A281187 A281188 KEYWORD nonn,look,easy AUTHOR Melissa Dennison, Apr 12 2017 EXTENSIONS Edited by N. J. A. Sloane, Apr 26 2017 STATUS approved

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Last modified July 12 23:28 EDT 2020. Contains 335669 sequences. (Running on oeis4.)