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%I #5 Jun 27 2018 13:15:59
%S 0,1,1,4,1,6,1,13,4,6,1,25,1,6,6,38,1,26,1,26,6,6
%N Number of subset-sum triangles with composite a subset-sum of the integer partition with Heinz number n.
%C 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.
%e We write positive subset-sum triangles in the form rootsum(branch,...,branch). The a(8) = 13 triangles:
%e 1(1(1,1,1))
%e 2(2(1,1,1))
%e 3(3(1,1,1))
%e 1(1(1),1(1,1))
%e 2(1(1),1(1,1))
%e 1(1(1),2(1,1))
%e 2(1(1),2(1,1))
%e 3(1(1),2(1,1))
%e 1(1(1,1),1(1))
%e 2(1(1,1),1(1))
%e 1(1(1),1(1),1(1))
%e 2(1(1),1(1),1(1))
%e 3(1(1),1(1),1(1))
%Y Cf. A063834, A262671, A269134, A276024, A281113, A299701, A301934, A301935, A316219, A316220, A316222.
%K nonn,more
%O 1,4
%A _Gus Wiseman_, Jun 27 2018
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