OFFSET
0,4
COMMENTS
We define a semi-sum of a multiset to be any sum of a 2-element submultiset. This is different from sums of pairs of elements. For example, 2 is the sum of a pair of elements of {1}, but there are no semi-sums.
EXAMPLE
The partitions of 6 and their a(6) = 17 semi-sums:
(6) ->
(51) -> 6
(42) -> 6
(411) -> 2,5
(33) -> 6
(321) -> 3,4,5
(3111) -> 2,4
(222) -> 4
(2211) -> 2,3,4
(21111) -> 2,3
(111111) -> 2
MATHEMATICA
Table[Total[Length[Union[Total/@Subsets[#, {2}]]]&/@IntegerPartitions[n]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 06 2023
EXTENSIONS
More terms from Alois P. Heinz, Nov 06 2023
STATUS
approved