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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 Table of n, a(n) for n=1..22. 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 Cf. A063834, A262671, A269134, A276024, A281113, A299701, A301934, A301935, A316219, A316220, A316222. Sequence in context: A232597 A197008 A344442 * A087652 A072195 A032310 Adjacent sequences: A316220 A316221 A316222 * A316224 A316225 A316226 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.)