A316222 Number of positive subset-sum triangles whose composite is a positive subset-sum of an integer partition of n.

1, 5, 20, 74, 258, 855, 2736, 8447

Offset

1,2

Comments

A positive subset-sum 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 subset-sums ((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 subset-sum triangles in the form rootsum(branch,...,branch). The a(2) = 5 positive subset-sum 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