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URL: https://oeis.org/A071651

⇱ A071651 - OEIS

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A071651
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.
9
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, 137, 254, 1597, 37, 79, 46, 121, 667, 106, 232, 407, 2212, 17, 38, 23, 30, 68, 13, 18, 20, 78, 465, 44, 153, 276, 1653, 19, 25, 27, 45, 91, 35, 55, 136, 703, 77, 120, 253, 435, 2278
OFFSET
0,3
COMMENTS
It seems that a(A014137(n)) = a(A014137(n)-1)+1 = A006894(n+1) for all n. - Antti Karttunen, Jul 30 2012
PROG
(Scheme) ;; Functions below show the essential idea. For a complete source, see "Alternative Catalan Orderings" OEIS Wiki page.
(define lexrank->arithrankA061579 (lexrank->arithrank-bijection packA061579))
(define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
(define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
(define (packA061579 x y) (/ (+ (expt (+ x y) 2) (* 3 x) y) 2))
CROSSREFS
Inverse permutation: A071652. Cf. also A014486, A061579, A071653, A071654.
Sequence in context: A175343 A239965 A072767 * A072658 A099864 A292956
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, May 30 2002
STATUS
approved