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 A089852 Involution of natural numbers induced by Catalan automorphism *A089852 acting on the binary trees/parenthesizations encoded by A014486/A063171. 14
 0, 1, 2, 3, 6, 5, 4, 7, 8, 16, 19, 15, 12, 13, 14, 11, 9, 17, 18, 10, 20, 21, 22, 44, 47, 53, 56, 60, 43, 52, 40, 31, 32, 41, 34, 35, 36, 42, 51, 39, 30, 33, 37, 28, 23, 45, 46, 24, 48, 49, 50, 38, 29, 25, 54, 55, 26, 57, 58, 59, 27, 61, 62, 63, 64, 128, 131, 137, 140, 144 (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). ...B...C...........B...A ....\./.............\./ .A...x....-->....C...x.................A..().........A...().. ..\./.............\./...................\./....-->....\./... ...x...............x.....................x.............x.... (a . (b . c)) -> (c . (b . a)) ______ (a . ()) ---> (a . ()) In terms of S-expressions, this automorphism swaps car and cddr of an S-exp if its length > 1, if possible, otherwise keeps it intact. 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 functions implementing this automorphism on list-structures/S-expressions, both constructive (*A089852) and destructive (*A089852!) versions:) (define (*A089852 s) (if (and (pair? s) (pair? (cdr s))) (cons (cddr s) (cons (cadr s) (car s))) s)) (define (*A089852! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) (else (let ((org_cddr (cddr s))) (set-cdr! (cdr s) (car s)) (set-car! s org_cddr) s)))) CROSSREFS a(n) = A069770(A089858(n)) = A089861(A069770(n)) = A057163(A089856(A057163(n))). Row 5 of A089840. 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: A130383 A130950 A122345 * A122308 A122307 A188568 Adjacent sequences:  A089849 A089850 A089851 * A089853 A089854 A089855 KEYWORD nonn AUTHOR Antti Karttunen, Nov 29 2003 EXTENSIONS Further comments and constructive implementation of Scheme-function (*A089852) added by Antti Karttunen, Jun 04 2011 STATUS approved

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)