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A154449
Signature permutation of a Catalan bijection induced by generator "a" of the rightward recursing instance of Basilica group wreath recursion: a = (1,b), b = s(1,a).
7
0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 11, 9, 10, 15, 14, 16, 17, 18, 19, 20, 21, 22, 32, 31, 34, 35, 36, 30, 33, 28, 23, 24, 29, 25, 26, 27, 40, 41, 39, 37, 38, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 91, 92, 90, 87, 88, 97, 96
OFFSET
0,3
COMMENTS
This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the rightmost tip of the tree along the 111... ray, so that the last vertex whose descendants are swapped, is the right-hand side child of the root and the root itself is fixed. Specifically, *A154449 = psi(A154439), where the isomorphism psi is given in A153141 (see further comments there).
PROG
(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154449! s) (if (pair? s) (*A154451! (cdr s))) s)
CROSSREFS
Inverse: A154450. a(n) = A154455(A069768(n)) = A057163(A154453(A057163(n))). Cf. A154451.
Sequence in context: A154122 A089850 A154450 * A122304 A122303 A130341
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 17 2009
STATUS
approved