A071163 A014486-indices for rooted binary trees with height equal to number of internal vertices. (Binary trees where at each internal vertex at least the other child is leaf.)

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 17, 18, 21, 22, 23, 24, 26, 27, 31, 32, 35, 36, 45, 46, 49, 50, 58, 59, 63, 64, 65, 66, 68, 69, 73, 74, 77, 78, 87, 88, 91, 92, 100, 101, 105, 106, 129, 130, 133, 134, 142, 143, 147, 148, 170, 171, 175, 176, 189, 190, 195, 196, 197

Offset: 0

Author

Antti Karttunen, May 14 2002

Keywords

• nonn

Comments

This subset of integers is closed by the actions of A069770, A057163, A069767, A069768, A122353, A122354, A122301, A122302, etc. (meaning, e.g., that A069767(a(n)) is a member from this sequence for all n), that is, by any Catalan bijection which is an image of some element of the automorphism group of infinite binary tree (the latter in a sense given by Grigorchuk, et al., being isomorphic to an infinitely iterated wreath product of cyclic groups of two elements). See the comments about the isomorphism "psi" given at A153141.

a(n) could be probably computed directly from the binary expansion of n by using a (somewhat) similar ranking function as given in A209640, but utilizing A009766 instead of A007318.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65535

Formula

a(n) = A080300(A071162(n)).