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 A057506 Signature-permutation of a Catalan Automorphism: (inverse of) "Donaghey's map M", acting on the parenthesizations encoded by A014486. 41
 0, 1, 3, 2, 8, 6, 7, 5, 4, 22, 19, 20, 15, 14, 21, 16, 18, 13, 11, 17, 12, 10, 9, 64, 60, 61, 52, 51, 62, 53, 55, 41, 39, 54, 40, 38, 37, 63, 56, 57, 43, 42, 59, 47, 50, 36, 33, 48, 34, 29, 28, 58, 44, 49, 35, 30, 46, 32, 27, 25, 45, 31, 26, 24, 23, 196, 191, 192, 178, 177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is inverse of A057505, which is a signature permutation of Catalan automorphism (bijection) known as "Donaghey's map M". See A057505 for more comments, links and references. LINKS Antti Karttunen, Table of n, a(n) for n = 0..23713 A. Karttunen (et al) at OEIS Wiki, Maple implementations of CatalanRankGlobal, CatalanSequences, car, cdr, binexp2pars and pars2binexp functions A. Karttunen at OEIS WIki, Scheme implementations of CatalanRankSexp and CatalanUnrankSexp Indranil Ghosh, Python program for computing this sequence (after the functions mentioned in the OEIS wiki) FORMULA a(n) = A057163(A057164(n)). a(n) = A057163(A057505(A057163(n))) = A057164(A057505(A057164(n))). MAPLE map(CatalanRankGlobal, map(DonagheysA057506, CatalanSequences(196))); # Where CatalanSequences(n) gives the terms A014486(0..n). DonagheysA057506 := n -> pars2binexp(deepreverse(DonagheysA057505(deepreverse(binexp2pars(n))))); DonagheysA057505 := h -> `if`((0 = nops(h)), h, [op(DonagheysA057505(car(h))), DonagheysA057505(cdr(h))]); # The following corresponds to automorphism A057164: deepreverse := proc(a) if 0 = nops(a) or list <> whattype(a) then (a) else [op(deepreverse(cdr(a))), deepreverse(a[1])]; fi; end; # The rest of required Maple-functions: see the given OEIS Wiki page. PROG (Scheme) (define (A057506 n) (CatalanRankSexp (*A057506 (CatalanUnrankSexp n)))) (define (*A057506 bt) (let loop ((lt bt) (nt (list))) (cond ((not (pair? lt)) nt) (else (loop (cdr lt) (cons nt (*A057506 (car lt)))))))) ;; Functions CatalanRankSexp and CatalanUnrankSexp can be found at OEIS Wiki page. CROSSREFS Inverse: A057505. Cf. A057161, A057162, A057163, A057164, A057501, A057502, A057503, A057504 (for similar signature permutations of simple Catalan automorphisms). Cf. A057507 (cycle counts). The 2nd, 3rd, 4th, 5th and 6th "powers" of this permutation: A071662, A071664, A071666, A071668, A071670. Row 12 of table A122287. Cf. also A014486, A080300, A080069, A080070. Sequence in context: A130361 A122338 A071667 * A086427 A125986 A131155 Adjacent sequences:  A057503 A057504 A057505 * A057507 A057508 A057509 KEYWORD nonn,look AUTHOR Antti Karttunen, Sep 03 2000 EXTENSIONS Entry revised by Antti Karttunen, May 30 2017 STATUS approved

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Last modified April 11 06:11 EDT 2021. Contains 342886 sequences. (Running on oeis4.)