This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367399 #6 Nov 20 2023 08:18:21
%S A367399 1,1,1,2,2,3,3,4,5,7,8,10,13,15,19,22,27,31,38,43,51,59,70,79,94,107,
%T A367399 124,143,165,188,218,248,283,324,369,419,476,540,610,691,778,878,987,
%U A367399 1111,1244,1399,1563,1750,1954,2184,2432,2714,3016,3358,3730,4143
%N A367399 Number of strict integer partitions of n whose length is not the sum of any two distinct parts.
%e A367399 The strict partition y = (6,4,2,1) has semi-sums {3,5,6,7,8,10}, which do not include 4, so y is counted under a(13).
%e A367399 The a(6) = 3 through a(13) = 15 strict partitions:
%e A367399 (6) (7) (8) (9) (10) (11) (12) (13)
%e A367399 (4,2) (4,3) (5,3) (5,4) (6,4) (6,5) (7,5) (7,6)
%e A367399 (5,1) (5,2) (6,2) (6,3) (7,3) (7,4) (8,4) (8,5)
%e A367399 (6,1) (7,1) (7,2) (8,2) (8,3) (9,3) (9,4)
%e A367399 (4,3,1) (8,1) (9,1) (9,2) (10,2) (10,3)
%e A367399 (4,3,2) (5,3,2) (10,1) (11,1) (11,2)
%e A367399 (5,3,1) (5,4,1) (5,4,2) (5,4,3) (12,1)
%e A367399 (6,3,1) (6,3,2) (6,4,2) (6,4,3)
%e A367399 (6,4,1) (6,5,1) (6,5,2)
%e A367399 (7,3,1) (7,3,2) (7,4,2)
%e A367399 (7,4,1) (7,5,1)
%e A367399 (8,3,1) (8,3,2)
%e A367399 (5,4,2,1) (8,4,1)
%e A367399 (9,3,1)
%e A367399 (6,4,2,1)
%t A367399 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&FreeQ[Total/@Subsets[#,{2}], Length[#]]&]], {n,0,15}]
%Y A367399 The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum, linear combination, or semi-sum of the parts. The current sequence is starred.
%Y A367399 sum-full sum-free comb-full comb-free semi-full semi-free
%Y A367399 -----------------------------------------------------------
%Y A367399 partitions: A367212 A367213 A367218 A367219 A367394 A367398
%Y A367399 strict: A367214 A367215 A367220 A367221 A367395 A367399*
%Y A367399 subsets: A367216 A367217 A367222 A367223 A367396 A367400
%Y A367399 ranks: A367224 A367225 A367226 A367227 A367397 A367401
%Y A367399 A000041 counts partitions, strict A000009.
%Y A367399 A002865 counts partitions whose length is a part, complement A229816.
%Y A367399 A365924 counts incomplete partitions, strict A365831.
%Y A367399 A236912 counts partitions with no semi-sum of the parts, ranks A364461.
%Y A367399 A237667 counts sum-free partitions, sum-full A237668.
%Y A367399 A366738 counts semi-sums of partitions, strict A366741.
%Y A367399 A367403 counts partitions without covering semi-sums, strict A367411.
%Y A367399 Triangles:
%Y A367399 A008284 counts partitions by length, strict A008289.
%Y A367399 A365541 counts subsets with a semi-sum k.
%Y A367399 A367404 counts partitions with a semi-sum k, strict A367405.
%Y A367399 Cf. A000700, A126796, A188431, A238628, A237113, A363225, A364272, A365658, A365918, A365925, A367410.
%K A367399 nonn
%O A367399 0,4
%A A367399 _Gus Wiseman_, Nov 19 2023