%I #6 May 01 2014 02:47:10

%S 0,2,10,12,42,52,56,170,178,204,212,232,240,682,722,738,812,852,868,

%T 920,936,976,992,2730,2762,2866,2898,2978,3010,3244,3276,3380,3412,

%U 3492,3524,3640,3672,3752,3784,3888,3920,4000,4032,10922,11082,11146

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

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

%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/tab9766.htm">Some notes on Catalan's Triangle</a>

%H <a href="/index/Par#parens">Index entries for sequences related to parenthesizing</a>

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

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

%p map(op,[seq(PalTotBalBinSequences(j),j=1..10)]);

%p PalTotBalBinSequences := n -> map(ReflectBinSeq,NonDivingLatticeSequences(n), n);

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

%K nonn

%O 0,2

%A _Antti Karttunen_, May 11 2001