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

Author

Gus Wiseman, May 16 2022

Keywords

• nonn

Examples

			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)
		

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.

Programs

Mathematica

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