A123714 Signature permutation of a nonrecursive Catalan automorphism: row 1786785 of table A089840.

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

Offset

0,3

Comments

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

.............................B...C............F...B......

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

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

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

.................................x...E............x...D..

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

..A...B.........C...A..............x...F............x...E

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

....x...C...-->...x...B..........()..x............()..x..

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

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

This is the last multiclause automorphism of total seven opened conses in the table A089840. The next nonrecursive automorphism, A089840[1786786], which consists of a single seven-node clause, swaps the first two toplevel elements (of a general plane tree, like *A072796 does), but only if A057515(n) > 6 and in other cases keeps the tree intact.

Links

A. Karttunen, Table of n, a(n) for n = 0..6917

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 (*A123714! s) (cond ((not (pair? s)) s) ((pair? (car s)) (let ((org_a (caar s))) (set-car! (car s) (cdr s)) (set-cdr! s (cdar s)) (set-cdr! (car s) org_a) s)) ((and (pair? (cdr s)) (pair? (cadr s)) (pair? (caadr s)) (pair? (caaadr s))) (let ((org_f (cddr s))) (set-cdr! (cdr s) (cdadr s)) (set-cdr! (cadr s) (cdaadr s)) (set-cdr! (caadr s) (cdr (caaadr s))) (set-cdr! (caaadr s) (car (caaadr s))) (set-car! (caaadr s) org_f) s)) (else s)))

Crossrefs

Inverse: A123713. Row 1786785 of A089840. Differs from A089857 for the first time at n=102, where a(n)=106, while A089857(n)=102.

Sequence in context: A220394 A082351 A122319 * A089857 A122316 A130990

Adjacent sequences: A123711 A123712 A123713 * A123715 A123716 A123717

Keyword

nonn

Author

Antti Karttunen, Oct 11 2006

Status

approved