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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
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
Sequence in context: A272086 A006650 A034535 * A273718 A094806 A289596
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 27 2018
STATUS
approved

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Last modified February 24 14:43 EST 2024. Contains 370305 sequences. (Running on oeis4.)