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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)

Index entries for signature-permutations of Catalan automorphisms

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 January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)