A364670 Number of strict integer partitions of n with a part equal to the sum of two distinct others. A variation of sum-full strict partitions.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 1, 4, 3, 7, 6, 10, 10, 14, 16, 24, 25, 34, 39, 48, 59, 71, 81, 103, 120, 136, 166, 194, 226, 260, 312, 353, 419, 473, 557, 636, 742, 824, 974, 1097, 1266, 1418, 1646, 1837, 2124, 2356, 2717, 3029, 3469, 3830, 4383, 4884, 5547

Offset: 0

Author

Gus Wiseman, Aug 03 2023

Keywords

• nonn

Examples

			The a(6) = 1 through a(16) = 10 strict partitions (A = 10):
  321  .  431  .  532   5321  642   5431  743   6432   853
                  541         651   6421  752   6531   862
                  4321        5421  7321  761   7431   871
                              6321        5432  7521   6532
                                          6431  9321   6541
                                          6521  54321  7432
                                          8321         7621
                                                       8431
                                                       A321
                                                       64321
		

Crossrefs

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

The non-strict version is A237113, complement A236912.

The non-binary complement is A237667, ranks A364532.

Allowing re-used parts gives A363226, non-strict A363225.

The non-binary version is A364272, non-strict A237668.

The complement is A364533, non-binary A364349.

A000041 counts integer partitions, strict A000009.

A008284 counts partitions by length, strict A008289.

A108917 counts knapsack partitions, strict A275972, ranks A299702.

A323092 counts double-free partitions, ranks A320340.

Cf. A007865, A025065, A093971, A111133, A151897, A240861, A325862, A364346, A364350, A364534.

Programs

Mathematica

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