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A316222 Number of positive subset-sum triangles whose composite is a positive subset-sum of an integer partition of n. 3
1, 5, 20, 74, 258, 855, 2736, 8447 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)