cp's OEIS Frontend

A366741 Number of semi-sums of strict integer partitions of n.

%I A366741 #6 Nov 07 2023 08:24:54
%S A366741 0,0,0,1,1,2,5,6,9,13,21,26,37,48,63,86,108,139,175,223,274,350,422,
%T A366741 527,638,783,939,1146,1371,1648,1957,2341,2770,3285,3867,4552,5353,
%U A366741 6262,7314,8529,9924,11511,13354,15423,17825,20529,23628,27116,31139,35615
%N A366741 Number of semi-sums of strict integer partitions of n.
%C A366741 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.
%e A366741 The strict partitions of 9 and their a(9) = 13 semi-sums:
%e A366741     (9) ->
%e A366741    (81) -> 9
%e A366741    (72) -> 9
%e A366741    (63) -> 9
%e A366741   (621) -> 3,7,8
%e A366741    (54) -> 9
%e A366741   (531) -> 4,6,8
%e A366741   (432) -> 5,6,7
%t A366741 Table[Total[Length[Union[Total/@Subsets[#, {2}]]]&/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n,0,30}]
%Y A366741 The non-strict non-binary version is A304792.
%Y A366741 The non-binary version is A365925.
%Y A366741 The non-strict version is A366738.
%Y A366741 A000041 counts integer partitions, strict A000009.
%Y A366741 A001358 lists semiprimes, squarefree A006881, conjugate A065119.
%Y A366741 A126796 counts complete partitions, ranks A325781, strict A188431.
%Y A366741 A276024 counts positive subset-sums of partitions, strict A284640.
%Y A366741 A365543 counts partitions with a subset summing to k, complement A046663.
%Y A366741 A365661 counts strict partitions w/ subset summing to k, complement A365663.
%Y A366741 A365924 counts incomplete partitions, ranks A365830, strict A365831.
%Y A366741 A366739 counts semi-sums of prime indices, firsts A367097.
%Y A366741 Cf. A008967, A122768, A299701, A364272, A364350, A365541, A365832, A366753.
%K A366741 nonn
%O A366741 0,6
%A A366741 _Gus Wiseman_, Nov 05 2023