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.

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, 253, 703, 136, 120, 55, 91, 1653, 276, 45, 153, 465, 78, 77, 35, 27, 44, 20, 25, 18, 68, 2212, 407, 30, 232, 667, 121, 19, 13, 23, 106, 46, 38, 79, 1597, 254, 17, 37, 137, 436

Offset

0,3

Comments

A071653(A014137(n-1)) = A072638(n) for all n > 0. - Paul D. Hanna, Jan 04 2007

Also seems that A071653(A014137(n)-1) = A006894(n) for all n > 0. - Antti Karttunen, Jul 30 2012

Links

Antti Karttunen, Table of n, a(n) for n = 0..2055

A. Karttunen, Alternative Catalan Orderings

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme functions below show the essential idea. For a complete source, see the "Alternative Catalan Orderings" OEIS Wiki page.)
(define lexrank->arithrankA001477 (lexrank->arithrank-bijection packA001477))
(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 (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))

Crossrefs

Inverse permutation: A071654. Cf. also A014486, A001477, A071651, A071652.

Sequence in context: A318280 A057977 A063549 * A227631 A246830 A268531

Adjacent sequences: A071650 A071651 A071652 * A071654 A071655 A071656

Keyword

nonn

Author

Antti Karttunen, May 30 2002

Status

approved