A061855 Symmetric totally balanced binary sequences: those terms of A014486 which are equal to their reversed complement.

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

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 * A358524 A144145 A075170

Adjacent sequences: A061852 A061853 A061854 * A061856 A061857 A061858

Keyword

nonn

Author

Antti Karttunen, May 11 2001

Status

approved