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A301934 Number of positive subset-sum trees of weight n. 4
1, 3, 14, 85, 586, 4331, 33545, 268521, 2204249 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..9.

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))

CROSSREFS

Cf. A000108, A000712, A108917, A122768, A262671, A262673, A275972, A276024, A284640, A299701, A301854, A301855, A301856, A301935.

Sequence in context: A111538 A324237 A230218 * A160881 A263187 A213628

Adjacent sequences:  A301931 A301932 A301933 * A301935 A301936 A301937

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Mar 28 2018

STATUS

approved

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Last modified February 23 23:59 EST 2020. Contains 332195 sequences. (Running on oeis4.)