OFFSET
0,18
COMMENTS
For an integer partition y of n, we call a positive integer k <= n a non-subset-sum iff there is no submultiset of y summing to k.
Is column k = n - 7 given by A325695?
EXAMPLE
Triangle begins:
1
1 0
0 1 0
1 0 1 0
0 1 0 1 0
0 0 2 0 1 0
1 0 0 2 0 1 0
1 0 0 0 3 0 1 0
0 1 1 0 0 3 0 1 0
0 0 3 0 0 0 4 0 1 0
1 0 0 2 2 0 0 4 0 1 0
1 0 0 0 5 0 0 0 5 0 1 0
2 0 0 0 0 5 2 0 0 5 0 1 0
2 0 1 0 0 0 8 0 0 0 6 0 1 0
1 1 3 0 0 0 0 7 3 0 0 6 0 1 0
2 0 4 0 1 0 0 0 12 0 0 0 7 0 1 0
1 1 2 2 3 1 0 0 0 11 3 0 0 7 0 1 0
2 0 3 0 7 0 1 0 0 0 16 0 0 0 8 0 1 0
3 0 0 2 6 3 3 1 0 0 0 15 4 0 0 8 0 1 0
Row n = 12: counts the following partitions:
(6,3,2,1) . . . . (9,2,1) (6,5,1) . . (11,1) . (12) .
(5,4,2,1) (8,3,1) (6,4,2) (10,2)
(7,4,1) (9,3)
(7,3,2) (8,4)
(5,4,3) (7,5)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[Complement[Range[n], Total/@Subsets[#]]]==k&]], {n, 0, 10}, {k, 0, n}]
CROSSREFS
The complement (positive subset-sums) is also A365545 with rows reversed.
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Sep 24 2023
STATUS
approved