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%I #4 May 01 2014 02:47:42
%S 1,2,2,3,3,3,3,4,4,3,4,4,5,4,4,4,5,5,5,5,4,4,5,6,5,6,5,4,4,5,6,6,6,6,
%T 5,4,4,5,6,6,7,6,6,5,4,5,5,6,6,7,7,6,6,5,5,5,6,6,6,7,7,7,6,6,6,5,5,6,
%U 7,6,7,7,7,7,6,7,6,5,5,6,7,7,7,7,7,7,7,7,7,6,5,5,6,7,7,8,7,7,7,7,8,7,7,6,5
%N The RASTxx transformation of the sequence A072643. The sizes of the parenthesizations produced by 'cons' combination A072764 & its transpose A072766.
%C Differs from A071673 first time at the position n=37, where A072768(37) = 4, while A071673(37) = 5. RASTxx(A072768) differs from A071673 first time at the position n=704, which leads to conjecture that the repeated applications of RASTxx starting from A072643 converge towards A071673, the fixed point of RASTxx transformation.
%C Each value v occurs A000108(v) times. (The term a(0)=0 is not explicitly listed here as to get a better looking triangle).
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (Includes the complete Scheme source for computing this sequence)
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a> (Maple code for RASTxx transform)
%o (Scheme) (define (A072768 n) (cond ((zero? n) n) (else (+ 1 (A072643 (A025581 (-1+ n))) (A072643 (A002262 (-1+ n)))))))
%Y Same triangle computed modulo 2: A072770. Permutations: A072643, A071673, A072644, A072645, A072660, A072789. Cf. also A072769, A025581, A002262.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Jun 12 2002
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