A364533 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..57.

EXAMPLE

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

MATHEMATICA

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

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.

Sequence in context: A244800 A275972 A364349 * A090492 A325768 A371736

Adjacent sequences: A364530 A364531 A364532 * A364534 A364535 A364536

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 02 2023

STATUS

approved