

A316223


Number of subsetsum triangles with composite a subsetsum of the integer partition with Heinz number n.


6



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

1,4


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


LINKS

Table of n, a(n) for n=1..22.


EXAMPLE

We write positive subsetsum 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.
Sequence in context: A113520 A232597 A197008 * A087652 A072195 A032310
Adjacent sequences: A316220 A316221 A316222 * A316224 A316225 A316226


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jun 27 2018


STATUS

approved



