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.

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

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 "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

Adjacent sequences: A071648 A071649 A071650 * A071652 A071653 A071654

Keyword

nonn,look

Author

Antti Karttunen, May 30 2002

Status

approved