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 A123492 An involution of nonnegative integers: signature permutation of a nonrecursive Catalan automorphism which swaps the sides of a binary tree if the left subtree of either the left or right hand side toplevel subtree is not empty and otherwise keeps the binary tree intact. 8
 0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 10, 20, 21, 22, 14, 19, 16, 17, 18, 15, 11, 12, 13, 23, 24, 25, 26, 27, 54, 55, 57, 58, 59, 61, 62, 63, 64, 37, 38, 53, 56, 60, 42, 51, 44, 45, 46, 47, 48, 49, 50, 43, 52, 39, 28, 29, 40, 30, 31, 32, 41, 33, 34, 35, 36, 65, 66, 67, 68, 69, 70, 71 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This automorphism effects the following transformation on the unlabeled rooted plane binary trees (letters A, B, C and D refer to arbitrary subtrees located on those nodes.) .....B...C.....B...C...........A...B.............A...B... ......\./.......\./.............\./...............\./.... .......x...D.....x...D...........x...C.............x...C. ........\./.......\./.............\./...............\./.. .....A...x...-->...x...A...........x...D...-->...D...x... ......\./...........\./.............\./...........\./.... .......x.............x...............x.............x..... LINKS PROG (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123492! s) (cond ((null? s) s) ((and (pair? (cdr s)) (pair? (cadr s))) (*A069770! s)) ((and (pair? (car s)) (pair? (caar s))) (*A069770! s))) s) CROSSREFS Row 79361 of A089840. Used to construct A123493, A123494, A123715 and A123716. Cf. A069770. Sequence in context: A191541 A122398 A222247 * A123493 A123715 A082313 Adjacent sequences:  A123489 A123490 A123491 * A123493 A123494 A123495 KEYWORD nonn AUTHOR Antti Karttunen, Oct 11 2006 STATUS approved

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