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 A384319 #5 May 28 2025 09:17:12
%S A384319 0,0,0,1,1,0,2,3,1,0,4,4,4,2,0,6,7,8,8,3,2,9,9,14,13,6,7,3,15,13,20
%N A384319 Number of strict integer partitions of n with exactly two possible ways to choose disjoint strict partitions of each part.
%e A384319 For y = (5,4,2) we have choices ((5),(4),(2)) and ((5),(3,1),(2)), so y is counted under a(11).
%e A384319 The a(3) = 1 through a(11) = 4 partitions:
%e A384319 (3) (4) . (4,2) (4,3) (6,2) . (5,3,2) (5,4,2)
%e A384319 (5,1) (5,2) (5,4,1) (6,3,2)
%e A384319 (6,1) (6,3,1) (7,3,1)
%e A384319 (7,2,1) (8,2,1)
%t A384319 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Length[pof[#]]==2&]],{n,0,30}]
%Y A384319 The case of a unique choice is A179009, ranks A383707.
%Y A384319 Choices of this type for each prime index are counted by A383706.
%Y A384319 The non-strict version for at least one choice is A383708, ranks A382913.
%Y A384319 The non-strict version for no choices is A383710, ranks A382912.
%Y A384319 The non-strict version for more than one choice is A384317, ranks A384321.
%Y A384319 The version for at least one choice is A384322, counted by A384318.
%Y A384319 The non-strict version is A384323, ranks A384347.
%Y A384319 These partitions are ranked by A384390.
%Y A384319 A239455 counts Look-and-Say or section-sum partitions, ranks A351294 or A381432.
%Y A384319 A351293 counts non Look-and-Say or non section-sum partitions, ranks A351295 or A381433.
%Y A384319 Cf. A098859, A279375, A299200, A317142, A357982, A381454, A383533, A383711, A384320.
%K A384319 nonn,more
%O A384319 0,7
%A A384319 _Gus Wiseman_, May 28 2025