A384319 Number of strict integer partitions of n with exactly two possible ways to choose disjoint strict partitions of each part.

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

Offset

0,7

Links

Table of n, a(n) for n=0..30.

Example

For y = (5,4,2) we have choices ((5),(4),(2)) and ((5),(3,1),(2)), so y is counted under a(11).
The a(3) = 1 through a(11) = 4 partitions:
  (3)  (4)  .  (4,2)  (4,3)  (6,2)  .  (5,3,2)  (5,4,2)
               (5,1)  (5,2)            (5,4,1)  (6,3,2)
                      (6,1)            (6,3,1)  (7,3,1)
                                       (7,2,1)  (8,2,1)

Mathematica

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[pof[#]]==2&]], {n, 0, 30}]

Crossrefs

The case of a unique choice is A179009, ranks A383707.

Choices of this type for each prime index are counted by A383706.

The non-strict version for at least one choice is A383708, ranks A382913.

The non-strict version for no choices is A383710, ranks A382912.

The non-strict version for more than one choice is A384317, ranks A384321.

The version for at least one choice is A384322, counted by A384318.

The non-strict version is A384323, ranks A384347.

These partitions are ranked by A384390.

A239455 counts Look-and-Say or section-sum partitions, ranks A351294 or A381432.

A351293 counts non Look-and-Say or non section-sum partitions, ranks A351295 or A381433.

Cf. A098859, A279375, A299200, A317142, A357982, A381454, A383533, A383711, A384320.

Sequence in context: A368486 A178245 A338753 * A167666 A115352 A275808

Adjacent sequences: A384316 A384317 A384318 * A384320 A384321 A384322

Keyword

nonn,more

Author

Gus Wiseman, May 28 2025

Status

approved