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A301934
Number of positive subset-sum trees of weight n.
4
1, 3, 14, 85, 586, 4331, 33545, 268521, 2204249
OFFSET
1,2
COMMENTS
A positive subset-sum tree with root x is either the symbol x itself, or is obtained by first choosing a positive subset-sum x <= (y_1,...,y_k) with k > 1 and then choosing a positive subset-sum tree with root y_i for each i = 1...k. The weight is the sum of the leaves. We write positive subset-sum trees in the form rootsum(branch,...,branch). For example, 4(1(1,3),2,2(1,1)) is a positive subset-sum tree with composite 4(1,1,1,2,3) and weight 8.
EXAMPLE
The a(3) = 14 positive subset-sum trees:
3 3(1,2) 3(1,1,1) 3(1,2(1,1))
2(1,2) 2(1,1,1) 2(1,1(1,1)) 2(1(1,1),1) 2(1,2(1,1))
1(1,2) 1(1,1,1) 1(1,1(1,1)) 1(1(1,1),1) 1(1,2(1,1))
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 28 2018
STATUS
approved