A071157 The zero-free, right-to-left factorial walk encoding for each rooted plane tree encoded by A014486. Sequence A071155 shown with factorial expansion (A007623).

0, 1, 11, 21, 111, 211, 121, 221, 321, 1111, 2111, 1211, 2211, 3211, 1121, 2121, 1221, 2221, 3221, 1321, 2321, 3321, 4321, 11111, 21111, 12111, 22111, 32111, 11211, 21211, 12211, 22211, 32211, 13211, 23211, 33211, 43211, 11121, 21121, 12121

Offset: 0

Author

Antti Karttunen, May 14 2002

Keywords

• nonn
• fini

Comments

Apart from the initial term (0, which encodes the null tree), if we scan the digits from the right (the least significant digit which is always 1) to the left (the most significant), then each successive digit to the left is at most one greater than the previous and never less than one.

Note: this finite decimal representation works only up to the 23712nd term, as the 23713rd such walk is already (10,9,8,7,6,5,4,3,2,1). The sequence A071158 shows the initial portion of this sequence sorted.

Links

• C. Banderier, A. Denise, P. Flajolet, M. Bousquet-Mélou et al., Generating Functions for Generating Trees, Discrete Mathematics 246(1-3), March 2002, pp. 29-55.
• A. Karttunen, Gatomorphisms and other excursions amidst the plane trees and parenthesizations (Includes the complete Scheme program for computing this sequence)

Crossrefs

Corresponding Łukasiewicz words: A071153.

Essentially the same as A071159 but with digits reversed.

Formula

a(n) = A007623(A071155(n)).