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A154122 Signature permutation of a Catalan bijection: row 3747 of A089840. 6
0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 9, 10, 11, 15, 14, 16, 17, 18, 19, 20, 21, 22, 31, 32, 34, 35, 36, 23, 24, 25, 26, 27, 28, 29, 30, 33, 40, 41, 37, 38, 39, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 87, 88, 90, 91, 92, 96, 97 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This bijection of binary trees can be obtained by applying bijection *A074680 to the right hand side subtree and leaving the left hand side subtree intact. See also comments at A154121.

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

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

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

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

.A...x...........A...x.................A...x.........A...x....

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

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

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

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

or (a . (() . c)) -> (a . (c . ())) 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 (*A154122! s) (if (pair? s) (*A074680! (cdr s))) s)

CROSSREFS

Inverse: A154121. a(n) = A069770(A089866(A069770(n))). Cf. A154124.

Sequence in context: A216250 A154121 A130375 * A089850 A154450 A154449

Adjacent sequences:  A154119 A154120 A154121 * A154123 A154124 A154125

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 06 2009

STATUS

approved

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