A129593 Prime-factorization encoded partition codes for the Łukasiewicz-words in A071153.

1, 2, 4, 3, 8, 9, 9, 9, 5, 16, 27, 27, 6, 25, 27, 25, 6, 27, 25, 25, 25, 25, 7, 32, 81, 81, 18, 125, 81, 125, 18, 18, 15, 125, 15, 15, 49, 81, 125, 125, 15, 49, 18, 15, 18, 81, 125, 15, 125, 15, 49, 125, 49, 15, 125, 49, 15, 15, 125, 49, 49, 49, 49, 49, 11, 64, 243, 243, 54

Offset: 0

Author

Antti Karttunen, May 01 2007

Keywords

• nonn

Comments

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 Łukasiewicz-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.

Examples

			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.
		

Links

• A. Karttunen, Table of n, a(n) for n = 0..2055
• OEIS Wiki, Łukasiewicz words
• Index entries for sequences related to Łukasiewicz

Crossrefs

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.

Formula

Construction: remove zeros from the Łukasiewicz-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.