0,2

If the signature-permutation of a Catalan automorphism SP satisfies the condition A129593(SP(n)) = A129593(n) for all n, then it is called a Lukasiewicz-word permuting automorphism. In addition to all the automorphisms whose signature permutation satisfies the more restricted condition A127301(SP(n)) = A127301(n) for all n, this includes also certain automorphisms like *A072797 that do not preserve the non-oriented form of the general tree. A000041(n) distinct values occur in each range [A014137(n-1)..A014138(n-1)]. All natural numbers occur. Cf. A129599.

A. Karttunen, Table of n, a(n) for n = 0..2055

Construction: remove zeros from the Lukasiewicz-word of a general plane tree encoded by A014486(n) (i.e. A071153(n)), sort the numbers into ascending order, and interpreting it as a partition of a natural number, encode it in the manner explained in A129595.

The terms A071153(5..7) are 201, 210, and 120. After discarding zero, and sorting, each produces partition 1+2. Converting it to prime-exponents like explained in A129595, we get 2^0 * 3^2 = 9, thus a(5) = a(6) = a(7) = 9.

a(n) = a(A072797(n)).

Variant: A129599. To be computed: the position of the first and the last occurrence of n, the number of occurrences of each n.

Adjacent sequences: A129590 A129591 A129592 this_sequence A129594 A129595 A129596

Sequence in context: A111699 A067179 A048767 this_sequence A026166 A077624 A077632

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), May 01 2007