

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.


4



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
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OFFSET

0,3


COMMENTS

A071653(A014137(n1)) = 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>arithrankbijection packA001477))
(define (lexrank>arithrankbijection packfun) (lambda (n) (rankbintree (binexp>parenthesization (A014486 n)) packfun)))
(define (rankbintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rankbintree (car bt) packfun) (rankbintree (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



