A316223 Number of subset-sum triangles with composite a subset-sum of the integer partition with Heinz number n.

0, 1, 1, 4, 1, 6, 1, 13, 4, 6, 1, 25, 1, 6, 6, 38, 1, 26, 1, 26, 6, 6

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. The composite of a triangle is (r, g_1 + ... + g_k) where + is multiset union.

Examples

			We write positive subset-sum triangles in the form rootsum(branch,...,branch). The a(8) = 13 triangles:
  1(1(1,1,1))
  2(2(1,1,1))
  3(3(1,1,1))
  1(1(1),1(1,1))
  2(1(1),1(1,1))
  1(1(1),2(1,1))
  2(1(1),2(1,1))
  3(1(1),2(1,1))
  1(1(1,1),1(1))
  2(1(1,1),1(1))
  1(1(1),1(1),1(1))
  2(1(1),1(1),1(1))
  3(1(1),1(1),1(1))
		

Crossrefs

Cf. A063834, A262671, A269134, A276024, A281113, A299701, A301934, A301935, A316219, A316220, A316222.