A072636 - OEIS

A072636

Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA054238tr as the packing bijection N X N -> N.

0, 1, 2, 3, 5, 6, 4, 9, 11, 18, 21, 17, 66, 70, 7, 8, 10, 35, 41, 12, 33, 131, 139, 261, 274, 258, 4101, 4117, 22, 65, 69, 1030, 1090, 81, 1026, 16390, 16454, 20, 23, 19, 68, 72, 13, 14, 36, 521, 547, 42, 515, 8201, 8233, 15, 16, 34, 43, 129, 132, 137, 2059, 2179

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..59.

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 A072636 (lexrank->arithrank-bijection packA054238tr))

(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 (packA054238tr x y) (+ (A000695 y) (* 2 (A000695 x))))

CROSSREFS

Inverse permutation: A072637. Cf. also A014486, A000695, A054238, A071651, A072634, A072646, A072656, A072658, A072644.

Sequence in context: A195610 A342038 A082654 * A191741 A191665 A306233

Adjacent sequences: A072633 A072634 A072635 * A072637 A072638 A072639

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2002

STATUS

approved