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 A387329 #5 Sep 06 2025 07:05:42
%S A387329 0,0,1,1,2,3,6,8,12,18,26,35,50,67,92,122,164,214,282,364,472
%N A387329 Number of integer partitions of n such that it is not possible to choose a different constant integer partition of each part.
%e A387329 The a(2) = 1 through a(8) = 12 partitions:
%e A387329 (11) (111) (211) (311) (222) (511) (611)
%e A387329 (1111) (2111) (411) (2221) (2222)
%e A387329 (11111) (2211) (3211) (3311)
%e A387329 (3111) (4111) (4211)
%e A387329 (21111) (22111) (5111)
%e A387329 (111111) (31111) (22211)
%e A387329 (211111) (32111)
%e A387329 (1111111) (41111)
%e A387329 (221111)
%e A387329 (311111)
%e A387329 (2111111)
%e A387329 (11111111)
%t A387329 consptns[n_]:=Select[IntegerPartitions[n],SameQ@@#&];
%t A387329 Table[Length[Select[IntegerPartitions[n],Select[Tuples[consptns/@#],UnsameQ@@#&]=={}&]],{n,0,15}]
%Y A387329 For divisors instead of constant partitions we have A370320, complement A239312.
%Y A387329 For all (not just constant) partitions we have A387134, ranks A387577.
%Y A387329 The complement all partitions is A387328, ranks A387576.
%Y A387329 The complement strict partitions is A387178.
%Y A387329 For strict (not just constant) partitions we have A387137.
%Y A387329 These partitions are ranked by A387180.
%Y A387329 The complement is A387330, ranked by A387181.
%Y A387329 A000005 counts constant integer partitions.
%Y A387329 A000009 counts strict integer partitions.
%Y A387329 A000041 counts integer partitions.
%Y A387329 Cf. A052335, A063834, A335448, A355739, A387110, A387115.
%K A387329 nonn,more,new
%O A387329 0,5
%A A387329 _Gus Wiseman_, Sep 05 2025