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

Author

Antti Karttunen, May 11 2001

Keywords

• nonn

Comments

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

Examples

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

Links

• A. Karttunen, Some notes on Catalan's Triangle
• Index entries for sequences related to parenthesizing

Crossrefs

Obtained by "reflecting" the terms of A061854. Cf. also A035928 (ReflectBinSeq), A061856, A069766.

Programs

Maple

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

Formula

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