

A316222


Number of positive subsetsum triangles whose composite is a positive subsetsum of an integer partition of n.


3




OFFSET

1,2


COMMENTS

A positive subsetsum is a pair (h,g), where h is a positive integer and g is an integer partition, such that some submultiset of g sums to h. A triangle consists of a root sum r and a sequence of positive subsetsums ((h_1,g_1),...,(h_k,g_k)) such that the sequence (h_1,...,h_k) is weakly decreasing and has a submultiset summing to r.


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

We write positive subsetsum triangles in the form rootsum(branch,...,branch). The a(2) = 5 positive subsetsum triangles:
2(2(2))
1(1(1,1))
2(2(1,1))
1(1(1),1(1))
2(1(1),1(1))


CROSSREFS

Cf. A063834, A262671, A269134, A276024, A281113, A301934, A301935, A316219, A316220.
Sequence in context: A272086 A006650 A034535 * A273718 A094806 A289596
Adjacent sequences: A316219 A316220 A316221 * A316223 A316224 A316225


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jun 27 2018


STATUS

approved



