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 A089856 Involution of natural numbers induced by Catalan Automorphism *A089856 acting on the binary trees/parenthesizations encoded by A014486/A063171. 12
 0, 1, 2, 3, 4, 5, 8, 7, 6, 9, 10, 11, 12, 13, 21, 22, 20, 17, 18, 19, 16, 14, 15, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 58, 59, 62, 63, 64, 57, 61, 54, 45, 46, 55, 48, 49, 50, 56, 60, 53, 44, 47, 51, 42, 37, 38, 52, 43, 39, 40, 41, 65, 66, 67, 68, 69, 70, 71, 72 (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 refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node). .A...B...........C...B ..\./.............\./ ...x...C....-->....x...A...............()..A.........()..A.. ....\./.............\./.................\./....-->....\./... .....x...............x...................x.............x.... ((a . b) . c) -> ((c . b) . a) _____ (() . a) ---> (() . a) In terms of S-expressions, this automorphism swaps caar and cdr of an S-exp if possible, i.e., if car-side is not (). See the Karttunen OEIS-Wiki link for a detailed explanation of how to obtain a given integer sequence from this definition. LINKS A. Karttunen, Catalan Automorphisms A. Karttunen, C-program for computing this sequence PROG (Scheme function implementing this automorphism on list-structures/S-expressions, both constructive (*A089856) and destructive (*A089856!) versions:) (define (*A089856 s) (if (and (pair? s) (pair? (car s))) (cons (cons (cdr s) (cdar s)) (caar s)) s)) (define (*A089856! s) (cond ((not (pair? s)) s) ((not (pair? (car s))) s) (else (let ((org_caar (caar s))) (set-car! (car s) (cdr s)) (set-cdr! s org_caar) s)))) CROSSREFS Row 10 of A089840. a(n) = A073269(A069770(n)) = A069770(A073270(n)) = A057163(A089852(A057163(n))). Number of cycles: A073191. Number of fixed points: A073190. Max. cycle size & LCM of all cycle sizes: A046698 (in each range limited by A014137 and A014138). Sequence in context: A130992 A122318 A130991 * A131151 A131152 A130939 Adjacent sequences:  A089853 A089854 A089855 * A089857 A089858 A089859 KEYWORD nonn AUTHOR Antti Karttunen, Nov 29 2003 EXTENSIONS Further comments and constructive implementation of Scheme-function (*A089856) added by Antti Karttunen, Jun 04 2011 STATUS approved

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Last modified December 7 03:27 EST 2019. Contains 329836 sequences. (Running on oeis4.)