A123696 Signature permutation of a nonrecursive Catalan automorphism: row 1653063 of table A089840.

0, 1, 3, 2, 8, 7, 4, 5, 6, 21, 22, 17, 18, 20, 9, 10, 11, 12, 13, 14, 15, 16, 19, 58, 59, 62, 63, 64, 45, 46, 48, 49, 50, 54, 55, 57, 61, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 51, 52, 53, 56, 60, 170, 171, 174, 175, 176

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.......C...D..............................

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

.A...B.............B...C......x...D....B..x............()...C......C..()...

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

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

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

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

See the comments at A123695.

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 (*A123696! s) (cond ((null? s) s) ((pair? (car s)) (*A074680! s)) ((pair? (cdr s)) (*A074680! (cdr s)) (*A069770! s))) s)

Crossrefs

Inverse: A123695. Row 1653063 of A089840. Variant of A074680.

Sequence in context: A245781 A239803 A083514 * A123500 A074689 A122331

Adjacent sequences: A123693 A123694 A123695 * A123697 A123698 A123699

Keyword

nonn

Author

Antti Karttunen, Oct 11 2006

Status

approved