

A061855


Symmetric totally balanced binary sequences: those terms of A014486 which are equal to their reversed complement.


6



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
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OFFSET

0,2


COMMENTS

These encode symmetric (palindromic) structures in many of the Catalan families, e.g. mountain ranges, parenthesizations, unlabeled rooted plane trees.


LINKS

Table of n, a(n) for n=0..45.
A. Karttunen, Some notes on Catalan's Triangle
Index entries for sequences related to parenthesizing


FORMULA

a(0) = 0 and the rest with the Maple function map(op, [seq(PalTotBalBinSequences(j), j=1..10)]);


EXAMPLE

E.g. the 45th term 11146 is 10101110001010 in binary and can be interpreted as a parenthesization: ( )( )((( )))( )( )


MAPLE

map(op, [seq(PalTotBalBinSequences(j), j=1..10)]);
PalTotBalBinSequences := n > map(ReflectBinSeq, NonDivingLatticeSequences(n), n);


CROSSREFS

Obtained by "reflecting" the terms of A061854. Cf. also A035928 (ReflectBinSeq), A061856, A069766.
Sequence in context: A075165 A209641 A209642 * A144145 A075170 A039571
Adjacent sequences: A061852 A061853 A061854 * A061856 A061857 A061858


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 11 2001


STATUS

approved



