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%I #4 Jun 27 2018 13:15:52
%S 1,5,20,74,258,855,2736,8447
%N Number of positive subset-sum triangles whose composite is a positive subset-sum of an integer partition of 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.
%e We write positive subset-sum triangles in the form rootsum(branch,...,branch). The a(2) = 5 positive subset-sum triangles:
%e 2(2(2))
%e 1(1(1,1))
%e 2(2(1,1))
%e 1(1(1),1(1))
%e 2(1(1),1(1))
%Y Cf. A063834, A262671, A269134, A276024, A281113, A301934, A301935, A316219, A316220.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Jun 27 2018
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