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A123714 Signature permutation of a nonrecursive Catalan automorphism: row 1786785 of table A089840. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 22 08:33 EST 2019. Contains 329389 sequences. (Running on oeis4.)