A365828 Number of strict integer partitions of 2n not containing n.

1, 1, 2, 3, 5, 8, 12, 18, 27, 39, 55, 78, 108, 148, 201, 270, 359, 475, 623, 811, 1050, 1351, 1728, 2201, 2789, 3517, 4418, 5527, 6887, 8553, 10585, 13055, 16055, 19685, 24065, 29343, 35685, 43287, 52387, 63253, 76200, 91605, 109897, 131575, 157231, 187539

Offset: 0

Author

Gus Wiseman, Sep 20 2023

Keywords

• nonn

Examples

			The a(0) = 1 through a(6) = 12 strict partitions:
  ()  (2)  (4)    (6)    (8)      (10)       (12)
           (3,1)  (4,2)  (5,3)    (6,4)      (7,5)
                  (5,1)  (6,2)    (7,3)      (8,4)
                         (7,1)    (8,2)      (9,3)
                         (5,2,1)  (9,1)      (10,2)
                                  (6,3,1)    (11,1)
                                  (7,2,1)    (5,4,3)
                                  (4,3,2,1)  (7,3,2)
                                             (7,4,1)
                                             (8,3,1)
                                             (9,2,1)
                                             (5,4,2,1)
		

Crossrefs

The complement is counted by A111133.

For non-strict partitions we have A182616, complement A000041.

A000009 counts strict integer partitions.

A046663 counts partitions with no submultiset summing to k, strict A365663.

A365827 counts strict partitions not of length 2, complement A140106.

Cf. A008967, A035363, A078408, A079122, A231429, A238628, A344415, A365659.

Programs

Mathematica

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

Formula

a(n) = A000009(2n) - A000009(n) + 1.