

A294150


Number of knapsack partitions of n that are also knapsack factorizations.


3



1, 1, 1, 2, 2, 4, 4, 6, 8, 10, 12, 13, 20, 20, 29, 30, 41, 41, 56, 53, 81, 75
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OFFSET

1,4


COMMENTS

a(n) is the number of finite multisets of positive integers summing to n such that every distinct submultiset has a different sum, and also every distinct submultiset has a different product.


LINKS



EXAMPLE

The a(12) = 13 partitions are:
(12),
(10 2), (9 3), (8 4), (7 5), (6 6),
(8 2 2), (7 3 2), (5 5 2), (5 4 3), (4 4 4),
(3 3 3 3),
(2 2 2 2 2 2).


MATHEMATICA

nn=22;
dubQ[y_]:=And[UnsameQ@@Times@@@Union[Rest@Subsets[y]], UnsameQ@@Plus@@@Union[Rest@Subsets[y]]];
Table[Length@Select[IntegerPartitions[n], dubQ], {n, nn}]


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



