%I #13 Apr 30 2014 01:53:47
%S 0,1,3,2,10,6,5,7,4,66,28,21,36,15,14,9,12,56,22,8,16,29,11,2278,435,
%T 253,703,136,120,55,91,1653,276,45,153,465,78,77,35,27,44,20,25,18,68,
%U 2212,407,30,232,667,121,19,13,23,106,46,38,79,1597,254,17,37,137,436
%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 A001477 as the packing bijection N x N -> N.
%C A071653(A014137(n-1)) = A072638(n) for all n > 0. - _Paul D. Hanna_, Jan 04 2007
%C Also seems that A071653(A014137(n)-1) = A006894(n) for all n > 0. - _Antti Karttunen_, Jul 30 2012
%H Antti Karttunen, <a href="/A071653/b071653.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 the "Alternative Catalan Orderings" OEIS Wiki page.)
%o (define lexrank->arithrankA001477 (lexrank->arithrank-bijection packA001477))
%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 (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
%Y Inverse permutation: A071654. Cf. also A014486, A001477, A071651, A071652.
%K nonn
%O 0,3
%A _Antti Karttunen_, May 30 2002
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