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%I #14 Apr 30 2014 01:53:47
%S 0,1,2,3,4,7,5,6,10,11,29,16,22,56,8,12,9,15,36,14,21,28,66,67,436,
%T 137,254,1597,37,79,46,121,667,106,232,407,2212,17,38,23,30,68,13,18,
%U 20,78,465,44,153,276,1653,19,25,27,45,91,35,55,136,703,77,120,253,435,2278
%N Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using the bivariate form of A061579 as the packing bijection N x N -> N.
%C It seems that a(A014137(n)) = a(A014137(n)-1)+1 = A006894(n+1) for all n. - _Antti Karttunen_, Jul 30 2012
%H Antti Karttunen, <a href="/A071651/b071651.txt">Table of n, a(n) for n = 0..2055</a>
%H A. Karttunen, <a href="https://oeis.org/wiki/Alternative_Catalan_Orderings">Alternative Catalan Orderings</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme functions below show the essential idea. For a complete source, see "Alternative Catalan Orderings" OEIS Wiki page.)
%o (define lexrank->arithrankA061579 (lexrank->arithrank-bijection packA061579))
%o (define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
%o (define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
%o (define (packA061579 x y) (/ (+ (expt (+ x y) 2) (* 3 x) y) 2))
%Y Inverse permutation: A071652. Cf. also A014486, A061579, A071653, A071654.
%K nonn,look
%O 0,3
%A _Antti Karttunen_, May 30 2002
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