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Search: id:A081706
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| A081706 |
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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. |
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+0
22
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| 2, 3, 10, 11, 14, 15, 18, 19, 26, 27, 34, 35, 42, 43, 46, 47, 50, 51, 58, 59, 62, 63, 66, 67, 74, 75, 78, 79, 82, 83, 90, 91, 98, 99, 106, 107, 110, 111, 114, 115, 122, 123, 130, 131, 138, 139, 142, 143, 146, 147, 154, 155, 162, 163, 170, 171, 174, 175, 178, 179, 186
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OFFSET
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1,1
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COMMENT
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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.
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]
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]
Also numbers n for which A010060(n+2)=A010060(n). [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jul 06 2009]
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LINKS
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J.-P. Allouche, Andre Arnold, Jean Berstel, Srecko Brlek, William Jockusch, Simon Plouffe and Bruce E. Sagan, A sequence related to that of Thue-Morse, Discrete Math., 139 (1995), 455-461.
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FORMULA
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a(2n-1)=2*A079523(n)=4*A003159(n)-2; a(2n)=4*A003159(n)-1. Note that a(2n)=1+a(2n-1).
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CROSSREFS
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Cf. A003159.
Cf. A079523.
Sequence in context: A007961 A060811 A146327 this_sequence A032804 A047473 A008509
Adjacent sequences: A081703 A081704 A081705 this_sequence A081707 A081708 A081709
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu) and Bruce E. Sagan, Apr 02 2003
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