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Search: id:A061855
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| A061855 |
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Symmetric totally balanced binary sequences: those terms of A014486 which are equal to their reversed complement. |
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+0
7
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| 0, 2, 10, 12, 42, 52, 56, 170, 178, 204, 212, 232, 240, 682, 722, 738, 812, 852, 868, 920, 936, 976, 992, 2730, 2762, 2866, 2898, 2978, 3010, 3244, 3276, 3380, 3412, 3492, 3524, 3640, 3672, 3752, 3784, 3888, 3920, 4000, 4032, 10922, 11082, 11146
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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These encode symmetric (palindromic) structures in many of the Catalan families, e.g. mountain ranges, parenthesizations, unlabeled rooted plane trees.
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LINKS
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A. Karttunen, Some notes on Catalan's Triangle
Index entries for sequences related to parenthesizing
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FORMULA
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a(0) = 0 and the rest with the Maple function map(op, [seq(PalTotBalBinSequences(j), j=1..10)]);
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EXAMPLE
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E.g. the 45th term 11146 is 10101110001010 in binary and can be interpreted as a parenthesization: ( )( )((( )))( )( )
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MAPLE
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map(op, [seq(PalTotBalBinSequences(j), j=1..10)]);
PalTotBalBinSequences := n -> map(ReflectBinSeq, NonDivingLatticeSequences(n), n);
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CROSSREFS
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Obtained by "reflecting" the terms of A061854. Cf. also A035928 (ReflectBinSeq), A061856, A069766.
Sequence in context: A166751 A071162 A075165 this_sequence A144145 A075170 A039571
Adjacent sequences: A061852 A061853 A061854 this_sequence A061856 A061857 A061858
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen May 11 2001
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