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%I #7 Mar 31 2012 14:02:28
%S 1,3,2,7,6,4,8,16,14,5,17,19,42,15,9,18,44,51,43,37,10,20,47,126,52,
%T 121,38,11,21,53,135,127,149,122,39,12,22,56,154,136,385,150,123,40,
%U 13,45,60,163,155,413,386,151,124,41,23,46,128,177,164,475,414,387,152
%N Tabular N X N -> N bijection induced by Lisp/Scheme function 'cons' combining the two planar binary trees/general trees/parenthesizations encoded by A014486(X) and A014486(Y).
%H <a href="/index/Li#ListFunsOfLisp">Index entries for the sequences induced by list functions of Lisp</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (with the complete Scheme source)
%o (Scheme functions showing the general idea:)
%o (define (A072764bi x y) (A080300 (parenthesization->binexp (cons (binexp->parenthesization (A014486 x)) (binexp->parenthesization (A014486 y))))))
%o (define (A072764 n) (cond ((zero? n) n) (else (A072764bi (A025581 (-1+ n)) (A002262 (-1+ n))))))
%Y Inverse permutation: A072765. a(n) = A069770(A072766(n)). Also transpose of A072766, i.e. a(n) = A072766(A038722(n)). The upper triangular region: A072773. Projection functions are A072771 ('car') & A072772 ('cdr'). The sizes of the corresponding Catalan structures: A072768. The first row: A057548, the first column: A072795, diagonal: A083938. Cf. also A080300, A025581, A002262.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_ Jun 12 2002
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