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%I #9 Jan 12 2024 08:18:58
%S 0,1,3,5,11,35,7,21,69,139,2059,43,547,8227,15,39,23,277,4117,71,85,
%T 1093,16453,32907,8388747,2187,526347,134219787,171,2091,555,131619,
%U 33554979,8235,8739,2105379,536879139,143,2063,47,551,8231,31,55,279,65813,16777493,4119,4373,1052693,268439573,79,103,87,341,4181,1095,1109
%N Recursive binary interleaving code for rooted plane binary trees, as ordered by A014486.
%C This encoding has a property that the greatest common subtree i.e. the intersect (or the least common supertree, the union) of any two trees can be obtained by simply computing the binary-AND (A004198) (or respectively: binary-OR, A003986) of the corresponding codes. See A082858-A082860.
%H Antti Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/ACO1.htm">Alternative Catalan Orderings</a> (with the complete Scheme source)
%e The empty tree . has code 0, the tree of two edges (and leaves) \/ has code 1 and in general tree's code is obtained by interleaving into odd and even bits (above bit-0, which is always 1 for nonempty trees) the codes for the left and right hand side subtrees of the tree.
%o (Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)
%o (define A082856 (compose-funs bin-interleave binexp->parenthesization A014486))
%o (define (bin-interleave bt) (cond ((not (pair? bt)) 0) (else (1+ (* 2 (+ (* 2 (A000695 (bin-interleave (car bt)))) (A000695 (bin-interleave (cdr bt)))))))))
%Y Inverse: A082857. Cf. A072634-A072637, A075173-A075174, A000695.
%K nonn
%O 0,3
%A _Antti Karttunen_, May 06 2003
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