A072634 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using A054238 as the pairing function N X N -> N.

0, 1, 3, 2, 11, 9, 4, 6, 5, 139, 131, 33, 41, 35, 12, 10, 8, 70, 66, 7, 17, 21, 18, 32907, 32779, 2051, 2179, 2059, 161, 137, 129, 8233, 8201, 43, 515, 547, 521, 140, 132, 34, 42, 36, 16, 14, 72, 16454, 16390, 68, 1026, 1090, 1030, 15, 13, 19, 81, 69, 23, 65

Offset

0,3

Links

Table of n, a(n) for n=0..57.

Antti Karttunen, Alternative Catalan Orderings

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme)
;; Functions below show the essential idea:
(define A072634 (lexrank->arithrank-bijection packA054238))
(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 (packA054238 x y) (+ (A000695 x) (* 2 (A000695 y))))

Crossrefs

Inverse permutation: A072635.

Cf. A014486, A000695, A054238, A071651, A072636, A072646, A072656, A072658, A072644.

Cf. also A296689.

Sequence in context: A275950 A276587 A180185 * A086194 A258386 A159610

Adjacent sequences: A072631 A072632 A072633 * A072635 A072636 A072637

Keyword

nonn

Author

Antti Karttunen, Jun 02 2002

Status

approved