%I A081706
%S A081706 2,3,10,11,14,15,18,19,26,27,34,35,42,43,46,47,50,51,58,59,62,63,66,67,
%T A081706 74,75,78,79,82,83,90,91,98,99,106,107,110,111,114,115,122,123,130,131,
%U A081706 138,139,142,143,146,147,154,155,162,163,170,171,174,175,178,179,186
%N A081706 Numbers n such that binary representation ends either in an odd number 
               of ones followed by one zero or in an even number of ones.
%C A081706 Values of k such that the Motzkin number A001006(k) is even. Values of 
               k such that the number of restricted hexagonal polyominoes with k+1 
               cells (A002212) is even.
%C A081706 Or union of sequences {2*A079523(n)+k}, k=0,1. A generalization see in 
               comment to A161639. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), 
               Jun 15 2009]
%C A081706 Or intersaction of sequences A121539 and {A121539(n)-1}. A generalization 
               see in comment to A161890. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), 
               Jul 03 2009]
%C A081706 Also numbers n for which A010060(n+2)=A010060(n). [From Vladimir Shevelev 
               (shevelev(AT)bgu.ac.il), Jul 06 2009]
%H A081706 J.-P. Allouche, Andre Arnold, Jean Berstel, Srecko Brlek, William Jockusch, 
               Simon Plouffe and Bruce E. Sagan, <a href="http://www-igm.univ-mlv.fr/
               ~berstel/Articles/Relative.ps">A sequence related to that of Thue-Morse</
               a>, Discrete Math., 139 (1995), 455-461.
%F A081706 a(2n-1)=2*A079523(n)=4*A003159(n)-2; a(2n)=4*A003159(n)-1. Note that 
               a(2n)=1+a(2n-1).
%Y A081706 Cf. A003159.
%Y A081706 Cf. A079523.
%Y A081706 Sequence in context: A007961 A060811 A146327 this_sequence A032804 A047473 
               A008509
%Y A081706 Adjacent sequences: A081703 A081704 A081705 this_sequence A081707 A081708 
               A081709
%K A081706 nonn
%O A081706 1,1
%A A081706 Emeric Deutsch (deutsch(AT)duke.poly.edu) and Bruce E. Sagan, Apr 02 
               2003