

A123503


An involution of nonnegative integers: signature permutation of a nonrecursive Catalan automorphism, row 253 of table A089840.


6



0, 1, 2, 3, 4, 6, 5, 8, 7, 9, 10, 14, 16, 19, 11, 15, 12, 21, 22, 13, 20, 17, 18, 23, 24, 25, 26, 27, 37, 38, 42, 44, 47, 51, 53, 56, 60, 28, 29, 39, 43, 52, 30, 40, 31, 58, 59, 32, 62, 63, 64, 33, 41, 34, 57, 61, 35, 54, 45, 46, 36, 55, 48, 49, 50, 65, 66, 67, 68, 69, 70, 71
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OFFSET

0,3


COMMENTS

This automorphism either swaps (if A057515(n) > 1) the first two toplevel elements (of a general plane tree, like *A072796 does) and otherwise (if n > 1, A057515(n)=1) swaps the sides of the left hand side subtree of the Sexpression (when viewed as a binary tree, like *A089854 does). This 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...C............A...B...........B...A
....\./...............\./..............\./.............\./
.A...x.....>.....B...x................x..()....>....x..()
..\./...............\./..................\./.............\./
...x....(A072796)....x....................x...(A089854)...x
(a . (b . c)) > (b . (a . c)) / ((a . b) . ()) > ((b . a) . ())
This is the first multiclause automorphism in table A089840 which cannot be represented as a composition of two smaller nonrecursive automorphisms, the property which is also shared by *A123499 and *A123500.


LINKS

Table of n, a(n) for n=0..71.
A. Karttunen, Prologprogram which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.
Index entries for signaturepermutations of Catalan automorphisms


PROG

(Scheme function, destructive implementation of this automorphism acting on Sexpressions:) (define (*A123503! s) (cond ((null? s) s) ((pair? (cdr s)) (*A072796! s)) (else (*A089854! s))) s)


CROSSREFS

Row 253 of A089840. Used to construct A123717 and A123718.
Sequence in context: A256988 A104650 A083179 * A123717 A123718 A121878
Adjacent sequences: A123500 A123501 A123502 * A123504 A123505 A123506


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 11 2006


STATUS

approved



