cp's OEIS Frontend

A071653 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.

%I A071653 #13 Apr 30 2014 01:53:47
%S A071653 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 A071653 253,703,136,120,55,91,1653,276,45,153,465,78,77,35,27,44,20,25,18,68,
%U A071653 2212,407,30,232,667,121,19,13,23,106,46,38,79,1597,254,17,37,137,436
%N A071653 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 A071653(A014137(n-1)) = A072638(n) for all n > 0. - _Paul D. Hanna_, Jan 04 2007
%C A071653 Also seems that A071653(A014137(n)-1) = A006894(n) for all n > 0. - _Antti Karttunen_, Jul 30 2012
%H A071653 Antti Karttunen, <a href="/A071653/b071653.txt">Table of n, a(n) for n = 0..2055</a>
%H A071653 A. Karttunen, <a href="https://oeis.org/wiki/Alternative_Catalan_Orderings">Alternative Catalan Orderings</a>
%H A071653 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A071653 (Scheme functions below show the essential idea. For a complete source, see the "Alternative Catalan Orderings" OEIS Wiki page.)
%o A071653 (define lexrank->arithrankA001477 (lexrank->arithrank-bijection packA001477))
%o A071653 (define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
%o A071653 (define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
%o A071653 (define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
%Y A071653 Inverse permutation: A071654. Cf. also A014486, A001477, A071651, A071652.
%K A071653 nonn
%O A071653 0,3
%A A071653 _Antti Karttunen_, May 30 2002