A123499 Signature permutation of a nonrecursive Catalan automorphism: rotate a binary tree left if possible, otherwise apply *A089863.

0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 21, 12, 13, 22, 11, 9, 10, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 31, 32, 59, 34, 35, 36, 60, 61, 62, 30, 33, 63, 28, 23, 24, 64, 29, 25, 26, 27, 107, 108, 109, 110, 111

Offset

0,3

Comments

This automorphism is illustrated below, where letters A, B and C refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node.

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

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

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

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

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

(a . (b . c)) --> ((a . b) . c) / ((a . b) . ()) --> (() . (b . a))

This automorphism cannot be represented as a composition of two smaller nonrecursive automorphisms. Cf. A123503.

Links

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

A. Karttunen, Prolog-program which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123499! s) (cond ((null? s) s) ((pair? (cdr s)) (*A074679! s)) (else (*A089863! s))) s)

Crossrefs

Inverse: A123500. Row 258 of A089840. Variant of A074679.

Sequence in context: A130965 A130997 A123695 * A082349 A082335 A074690

Adjacent sequences: A123496 A123497 A123498 * A123500 A123501 A123502

Keyword

nonn

Author

Antti Karttunen, Oct 11 2006

Status

approved