%I
%S 0,1,2,2,4,4,6,4,4,9,9,11,9,9,14,14,14,9,9,14,11,9,9,23,23,25,23,23,
%T 28,28,28,23,23,28,25,23,23,37,37,39,37,37,42,42,37,23,23,37,25,23,23,
%U 42,42,39,28,28,37,28,23,23,37,28,25,23,23,65,65,67,65,65,70,70,70,65
%N The first representative in A014486 for each equivalence class of nonoriented binary tree corresponding to the oriented (plane) binary tree encoded by A014486(n).
%C Any n that occurs in the sequence, occurs for the first time at n (i.e. a(n)=n), thus there are no cases where a(n) > n. A001190(n+1) distinct values occur in each range [A014137(n1)..A014138(n1)]. This sequence is similar to A127302 in that it maps all the plane binary trees which belong to the same equivalence class of nonoriented binary trees to one and same integer and likewise, every Catalan bijection whose signature permutation SP satisfies the condition mentioned in A127302, satisfies in a similar way A153835(SP(n)) = A153835(n).
%H A. Karttunen, <a href="/A153835/b153835.txt">Table of n, a(n) for n = 0..2055</a>
%o (MIT Scheme:) (define (*A153835! s) (cond ((pair? s) (*A153835! (car s)) (*A153835! (cdr s)) (if (= 1 (A154103bi (parenthesization>A014486 (car s)) (parenthesization>A014486 (cdr s)))) (*A069770! s)))) s)
%Y A127302(a(n)) = A127302(n) holds for all n. Cf. A154103, A069770.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 05 2009
