A072656 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA048680oA054238 as the packing bijection N X N -> N.

0, 1, 3, 2, 11, 6, 5, 7, 4, 100, 27, 24, 45, 14, 18, 10, 13, 62, 17, 8, 15, 28, 9, 1988, 477, 179, 1100, 116, 150, 61, 113, 2090, 147, 35, 189, 302, 58, 162, 44, 39, 73, 23, 34, 20, 102, 1229, 295, 29, 111, 680, 72, 21, 12, 26, 93, 38, 47, 70, 1292, 91, 16, 22, 117, 187

Offset

0,3

Links

Table of n, a(n) for n=0..63.

A. Karttunen, Gatomorphisms

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme functions below show the essential idea. For a complete source, follow the "Gatomorphisms" link.)
(define A072656 (lexrank->arithrank-bijection packA048680oA054238))
(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 (packA048680oA054238 x y) (A048680 (packA054238 x y)))
(define (packA054238 x y) (+ (A000695 x) (* 2 (A000695 y))))

Crossrefs

Inverse permutation: A072657. Cf. also A014486, A000695, A054238, A048680, A071651, A072634, A072636, A072646, A072658, A072660.

Sequence in context: A238398 A065014 A013945 * A330313 A191669 A344891

Adjacent sequences: A072653 A072654 A072655 * A072657 A072658 A072659

Keyword

nonn

Author

Antti Karttunen, Jun 02 2002

Status

approved