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A154124 Signature permutation of a Catalan bijection: row 3748 of A089840. 4
0, 1, 2, 3, 6, 4, 5, 7, 8, 16, 19, 9, 10, 11, 15, 14, 12, 17, 18, 13, 20, 21, 22, 44, 47, 53, 56, 60, 23, 24, 25, 26, 27, 28, 29, 30, 33, 43, 52, 37, 38, 39, 40, 42, 31, 45, 46, 32, 48, 49, 50, 41, 51, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 128, 131, 137, 140, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This bijection of binary trees is obtained in the following way. (Inverse of Thompson's B!):

.B...C...............C...D

..\./.................\./

...x...D....-->....B...x.................()..C ........A...()

....\./.............\./...................\./....-->....\./...

.A...x...........A...x.................A...x.........C...x....

..\./.............\./...................\./...........\./.....

...x...............x.....................x.............x......

..............................................................

That is, (a . ((b . c) . d)) -> (a . (b . (c . d)))

or (a . (() . c)) -> (c . (a . ())) if the former is not possible.

LINKS

A. Karttunen, Table of n, a(n) for n = 0..2055

Index entries for signature-permutations of Catalan automorphisms

PROG

(Destructive version of this automorphism in Scheme:) (define (*A154124! s) (if (and (pair? s) (pair? (cdr s)) (pair? (cadr s))) (*A074680! (cdr s)) (*A089853! s)) s)

CROSSREFS

Inverse: A154123. Cf. A154122.

Sequence in context: A131144 A131147 A130984 * A089853 A122306 A122309

Adjacent sequences:  A154121 A154122 A154123 * A154125 A154126 A154127

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 06 2009

STATUS

approved

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Last modified November 19 19:09 EST 2019. Contains 329323 sequences. (Running on oeis4.)