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

Author

Gus Wiseman, Jun 27 2018

Keywords

• nonn
• more

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.

Examples

			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.