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A316223 Number of subset-sum triangles with composite a subset-sum 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
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.
LINKS
EXAMPLE
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
Sequence in context: A232597 A197008 A344442 * A087652 A072195 A032310
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 27 2018
STATUS
approved

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Last modified February 22 06:21 EST 2024. Contains 370240 sequences. (Running on oeis4.)