A364533 Number of strict integer partitions of n containing the sum of no pair of distinct parts. A variation of sum-free strict partitions.

1, 1, 1, 2, 2, 3, 3, 5, 5, 8, 7, 11, 11, 15, 15, 21, 22, 28, 32, 38, 40, 51, 55, 65, 74, 83, 94, 111, 119, 136, 160, 174, 196, 222, 252, 273, 315, 341, 391, 425, 477, 518, 602, 636, 719, 782, 886, 944, 1073, 1140, 1302, 1380, 1553, 1651, 1888, 1995, 2224, 2370

Offset: 0

Author

Gus Wiseman, Aug 02 2023

Keywords

• nonn

Examples

			The a(1) = 1 through a(12) = 11 partitions (A..C = 10..12):
  1   2   3    4    5    6    7     8     9     A     B     C
          21   31   32   42   43    53    54    64    65    75
                    41   51   52    62    63    73    74    84
                              61    71    72    82    83    93
                              421   521   81    91    92    A2
                                          432   631   A1    B1
                                          531   721   542   543
                                          621         632   732
                                                      641   741
                                                      731   831
                                                      821   921
		

Crossrefs

For subsets of {1..n} we have A085489, complement A088809.

The non-strict version is A236912, complement A237113, ranked by A364461.

Allowing re-used parts gives A364346.

The non-binary version is A364349, non-strict A237667 (complement A237668).

The linear combination-free version is A364350.

The complement in strict partitions is A364670, w/ re-used parts A363226.

A000041 counts integer partitions, strict A000009.

A008284 counts partitions by length, strict A008289.

A108917 counts knapsack partitions, strict A275972.

A151897 counts sum-free subsets, complement A364534.

A323092 counts double-free partitions, ranks A320340.

Cf. A007865, A025065, A240861, A325862, A326083, A364272, A364345, A364347.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, Total/@Subsets[#,{2}]] == {}&]],{n,0,30}]