A072088 Permutation of natural numbers induced by the automorphism gt-bf->df (switch from the Breadth First to the Depth First coding for the general trees/parenthesizations) acting on the parenthesizations encoded by A014486.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 16, 17, 18, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 33, 30, 31, 32, 29, 34, 35, 36, 37, 51, 38, 56, 60, 42, 47, 44, 45, 46, 53, 48, 49, 50, 39, 41, 43, 54, 61, 40, 57, 58, 59, 52, 55, 62, 63, 64, 65, 66, 67, 68, 69, 70, 75

Offset

0,3

Comments

When restricted to the subset of plane binary trees, produces the automorphism A057117, with which this shares the property of "self-embeddability": each sub-permutation of the length A000108(n): 0; 1; 2,3; 4,5,6,7,8; 9,10,11,12,13,14,19,16,17,18,15,20,21,22; 23,24,25,26,27,28,33,30,31,32,29,34,35,36,37,51,38,56,60,42,47,44,45,46,53,48,49,50,39,41,43,54,61,40,57,58,59,52,55,62,63,64; starts with the same cycle-structure as the previous sub-permutation. (i.e. the terms from the first to the sixth are fixed, the 7th and 11th are transposed, etc.), thus allowing us to construct the permutation A072619 (A072621).

Links

Table of n, a(n) for n=0..71.

A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)

Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A072089. Cf. also A014486, A057117, A072619.

Sequence in context: A347620 A078107 A072089 * A023768 A023795 A032949

Adjacent sequences: A072085 A072086 A072087 * A072089 A072090 A072091

Keyword

nonn

Author

Antti Karttunen, Jun 25 2002

Status

approved