A153830 Index sequence to A089840: positions of bijections that preserve A127302 (the non-oriented form of binary trees) and whose behavior does not depend on whether there are internal or terminal nodes (leaves) in the neighborhood of any vertex.

0, 1, 3, 7, 15, 21, 27, 46, 92, 114, 149, 169, 225, 251, 299, 400, 638, 753, 1233, 1348, 1705, 1823, 1992, 2097, 2335, 2451, 2995, 3128, 3485, 3607, 3677, 3771, 4214, 4307, 4631, 5254, 6692, 7393, 10287, 10988, 13145, 13860, 20353, 21054

Offset: 0

Author

Antti Karttunen, Jan 07 2009

Keywords

• nonn

Comments

These elements form a subgroup in A089840 (A089839) isomorphic to a group consisting of all finitely iterated wreath products of the form S_2 wr S_2 wr ... wr S_2 and each is an image of some finitary automorphism of an infinite binary tree. E.g. A089840(1) = *A069770 is an image of the generator A of Grigorchuk Group. See comments at A153246 and A153141.

The defining properties are propagated by all recursive transformations of A089840 which themselves do not behave differently depending whether there are internal or terminal vertices in the neighborhood of any vertex (at least the ones given in A122201-A122204, A122283-A122290, A130400-A130403), so this sequence gives also the corresponding positions in those tables.

Links

• A. Karttunen, Table of n, a(n) for n = 0..175
• A. Karttunen, C-program for computing the initial terms of this sequence

Crossrefs

Subset of A153829. Cf. also A153831, A153826, A153827, A153828, A153832, A153833.