A089865 Permutation of natural numbers induced by Catalan Automorphism *A089865 acting on the parenthesizations/binary trees encoded by A014486/A063171.

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 19, 20, 21, 16, 22, 17, 18, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 42, 43, 60, 61, 62, 44, 63, 45, 46, 47, 64, 48, 49, 50, 65, 66, 67, 68, 69

Offset

0,3

Comments

This bijection of binary trees is obtained when we apply bijection *A074679 to the left subtree and keep the right subtree intact.

....B...C.......A...B

.....\./.........\./

..A...x....-->....x...C.................A..().........()..A....

...\./.............\./...................\./....-->....\./.....

....x...D...........x...D.................x...C.........x...C..

.....\./.............\./...................\./...........\./...

......x...............x.....................x.............x....

...............................................................

Compare to A154121.

See "Catalan Automorphisms" OEIS-Wiki page for a detailed explanation how to obtain a given integer sequence from this definition.

Links

Table of n, a(n) for n=0..69.

A. Karttunen, Catalan Automorphisms

A. Karttunen, C-program for computing this sequence

Index entries for signature-permutations induced by Catalan automorphisms

Prog

(Scheme function implementing this automorphism on list-structures/S-expressions, both constructive (*A089865) and destructive (*A089865!) versions:)
(define (*A089865 s) (cond ((pair? s) (cons (*A074679 (car s)) (cdr s))) (else s)))
(define (*A089865! s) (if (pair? s) (*A074679! (car s))) s)

Crossrefs

Row 4207 of A089840. Inverse of A089866. a(n) = A069770(A154121(A069770(n))).

Number of cycles: A089844. Number of fixed-points: A005807 (prepended with two 1's). Max. cycle size: A089410. LCM of cycle sizes: A089845 (in each range limited by A014137 and A014138).

Sequence in context: A130372 A353825 A353824 * A089866 A089854 A154453

Adjacent sequences: A089862 A089863 A089864 * A089866 A089867 A089868

Keyword

nonn

Author

Antti Karttunen, Dec 20 2003

Extensions

Further comments and constructive version of Scheme-implementation added by Antti Karttunen, Jun 04 2011

Status

approved