A364670 - OEIS

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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

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OFFSET

0,11

LINKS

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

EXAMPLE

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

MATHEMATICA

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

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.

Sequence in context: A340760 A035626 A082587 * A060043 A298254 A337588

Adjacent sequences: A364667 A364668 A364669 * A364671 A364672 A364673

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 03 2023

STATUS

approved