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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.

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]=0; b[1]=1; b[2]=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 April 19 16:18 EDT 2019. Contains 322282 sequences. (Running on oeis4.)