A353501 Number of integer partitions of n with all parts and all multiplicities > 2.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 2, 3, 0, 0, 6, 2, 0, 6, 3, 2, 9, 2, 5, 11, 3, 5, 18, 6, 4, 20, 13, 8, 26, 10, 17, 37, 14, 16, 51, 23, 24, 58, 38, 32, 75, 44, 52, 100, 52, 59, 143, 75, 77, 159, 114, 112, 203, 132, 154, 266, 175

Offset

0,13

Links

Table of n, a(n) for n=0..70.

Example

The a(n) partitions for selected n (A = 10):
  n=9:   n=12:   n=21:      n=24:       n=30:
------------------------------------------------------
  (333)  (444)   (777)      (888)       (AAA)
         (3333)  (444333)   (6666)      (66666)
                 (3333333)  (444444)    (555555)
                            (555333)    (666444)
                            (4443333)   (777333)
                            (33333333)  (6663333)
                                        (55533333)
                                        (444333333)
                                        (3333333333)

Mathematica

Table[Length[Select[IntegerPartitions[n], Min@@#>2&&Min@@Length/@Split[#]>2&]], {n, 0, 30}]

Crossrefs

The version for only parts > 2 is A008483.

The version for only multiplicities > 2 is A100405.

The version for parts and multiplicities > 1 is A339222, ranked by A062739.

For prime parts and multiplicities we have A351982, compositions A353429.

The version for compositions is A353428 (partial A078012, A353400).

These partitions are ranked by A353502.

A000726 counts partitions with all mults <= 2, compositions A128695.

A004250 counts partitions with some part > 2, compositions A008466.

A137200 counts compositions with all parts and run-lengths <= 2.

Cf. A003242, A047966, A055923, A098859, A114901, A325534, A333755, A335464.

Sequence in context: A219487 A303907 A290870 * A353428 A244738 A331195

Adjacent sequences: A353498 A353499 A353500 * A353502 A353503 A353504

Keyword

nonn

Author

Gus Wiseman, May 16 2022

Status

approved