

A301935


Number of positive subsetsum trees whose composite a positive subsetsum of the integer partition with Heinz number n.


6



0, 1, 1, 2, 1, 3, 1, 10, 2, 3, 1, 21, 1, 3, 3, 58, 1, 21, 1, 21, 3, 3, 1, 164, 2, 3, 10, 21, 1, 34, 1, 373, 3, 3, 3, 218, 1, 3, 3, 161, 1, 7, 1, 5, 5, 3, 1, 1320, 2, 5, 3, 5, 1, 7, 3, 7, 3, 3, 1, 7, 1, 3, 4, 2558, 3, 7, 1, 5, 3, 6, 1, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). A positive subsetsum tree with root x is either the symbol x itself, or is obtained by first choosing a positive subsetsum x <= (y_1,...,y_k) with k > 1 and then choosing a positive subsetsum tree with root y_i for each i = 1...k. The composite of a positive subsetsum tree is the positive subsetsum x <= g where x is the root sum and g is the multiset of leaves. We write positive subsetsum trees in the form rootsum(branch,...,branch). For example, 4(1(1,3),2,2(1,1)) is a positive subsetsum tree with composite 4(1,1,1,2,3) and weight 8.


LINKS

Table of n, a(n) for n=1..72.
Gus Wiseman, The a(12) = 21 positive subsetsum trees.


CROSSREFS

Cf. A000108, A000712, A108917, A122768, A262671, A262673, A275972, A276024, A284640, A299701, A301854, A301855, A301856, A301934.
Sequence in context: A126761 A090559 A186725 * A237978 A098570 A122048
Adjacent sequences: A301932 A301933 A301934 * A301936 A301937 A301938


KEYWORD

nonn


AUTHOR

Gus Wiseman, Mar 28 2018


STATUS

approved



