cp's OEIS Frontend

A366753 Number of integer partitions of n without all different sums of two-element submultisets.

%I A366753 #7 Nov 08 2023 07:50:44
%S A366753 0,0,0,0,0,0,0,0,1,1,3,4,9,11,22,27,48,61,98,123,188,237,345,435,611,
%T A366753 765,1046,1305,1741,2165,2840,3502,4527,5562,7083,8650,10908,13255,
%U A366753 16545,20016,24763,29834,36587,43911,53514,63964,77445,92239,111015,131753
%N A366753 Number of integer partitions of n without all different sums of two-element submultisets.
%e A366753 The two-element submultisets of y = {1,1,1,2,2,3} are {1,1}, {1,2}, {1,3}, {2,2}, {2,3}, with sums 2, 3, 4, 4, 5, which are not all different, so y is counted under a(10).
%e A366753 The a(8) = 1 through a(13) = 11 partitions:
%e A366753   (3221)  (32211)  (4321)    (33221)    (4332)      (43321)
%e A366753                    (32221)   (43211)    (5331)      (53221)
%e A366753                    (322111)  (322211)   (5421)      (53311)
%e A366753                              (3221111)  (43221)     (54211)
%e A366753                                         (322221)    (332221)
%e A366753                                         (332211)    (432211)
%e A366753                                         (432111)    (3222211)
%e A366753                                         (3222111)   (3322111)
%e A366753                                         (32211111)  (4321111)
%e A366753                                                     (32221111)
%e A366753                                                     (322111111)
%t A366753 Table[Length[Select[IntegerPartitions[n],!UnsameQ@@Total/@Union[Subsets[#,{2}]]&]],{n,0,30}]
%Y A366753 Semiprime divisors are counted by A086971, distinct sums A366739.
%Y A366753 The non-binary complement is A108917, strict A275972, ranks A299702.
%Y A366753 These partitions have ranks A366740.
%Y A366753 The non-binary version is A366754, strict A316402, ranks A299729.
%Y A366753 A276024 counts positive subset-sums of partitions, strict A284640.
%Y A366753 A304792 counts subset-sum of partitions, strict A365925.
%Y A366753 A365543 counts partitions with a subset-sum k, complement A046663.
%Y A366753 A365661 counts strict partitions with a subset-sum k, complement A365663.
%Y A366753 A366738 counts semi-sums of partitions, strict A366741.
%Y A366753 A367096 lists semiprime divisors, row sums A076290.
%Y A366753 Cf. A002033, A001358, A006827, A008967, A122768, A126796, A365923, A365924, A367093, A367095.
%K A366753 nonn
%O A366753 0,11
%A A366753 _Gus Wiseman_, Nov 07 2023