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%I #5 May 01 2014 02:47:41
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,19,16,17,18,15,20,21,22,23,24,25,
%T 26,27,28,33,30,31,32,29,34,35,36,37,51,38,56,60,42,47,44,45,46,53,48,
%U 49,50,39,41,43,54,61,40,57,58,59,52,55,62,63,64,65,66,67,68,69,70,75
%N Permutation of natural numbers induced by the automorphism gt-bf->df (switch from the Breadth First to the Depth First coding for the general trees/parenthesizations) acting on the parenthesizations encoded by A014486.
%C When restricted to the subset of plane binary trees, produces the automorphism A057117, with which this shares the property of "self-embeddability": each sub-permutation of the length A000108(n): 0; 1; 2,3; 4,5,6,7,8; 9,10,11,12,13,14,19,16,17,18,15,20,21,22; 23,24,25,26,27,28,33,30,31,32,29,34,35,36,37,51,38,56,60,42,47,44,45,46,53,48,49,50,39,41,43,54,61,40,57,58,59,52,55,62,63,64; starts with the same cycle-structure as the previous sub-permutation. (i.e. the terms from the first to the sixth are fixed, the 7th and 11th are transposed, etc.), thus allowing us to construct the permutation A072619 (A072621).
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (Includes the complete Scheme program for computing this sequence)
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y Inverse permutation: A072089. Cf. also A014486, A057117, A072619.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 25 2002
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