A325862 - OEIS

A325862

Number of integer partitions of n such that every set of distinct parts has a different sum.

1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 34, 46, 58, 77, 93, 122, 146, 188, 217, 282, 327, 410, 470, 596, 673, 848, 947, 1178, 1325, 1629, 1798, 2213, 2444, 2962, 3247, 3935, 4292, 5149, 5579, 6674, 7247, 8590, 9221, 10964, 11804, 13870, 14843, 17480, 18675, 21866

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OFFSET

0,3

COMMENTS

A knapsack partition (A108917, A299702) is an integer partition such that every submultiset has a different sum. The one non-knapsack partition counted under a(4) is (2,1,1).

LINKS

Table of n, a(n) for n=0..49.

EXAMPLE

The a(1) = 1 through a(7) = 14 partitions:

(1) (2) (3) (4) (5) (6) (7)

(11) (21) (22) (32) (33) (43)

(111) (31) (41) (42) (52)

(211) (221) (51) (61)

(1111) (311) (222) (322)

(2111) (411) (331)

(11111) (2211) (421)

(3111) (511)

(21111) (2221)

(111111) (4111)

(22111)

(31111)

(211111)

(1111111)

The three non-knapsack partitions counted under a(6) are:

(2,2,1,1)

(3,1,1,1)

(2,1,1,1,1)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@Plus@@@Subsets[Union[#]]&]], {n, 0, 20}]

CROSSREFS

Dominates A108917.

Cf. A002033, A034444, A196723, A275972, A276024, A299702, A325592, A325856, A325863, A325864, A325865, A325877.

Sequence in context: A116480 A023026 A096778 * A280277 A102108 A105780

Adjacent sequences: A325859 A325860 A325861 * A325863 A325864 A325865

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 31 2019

STATUS

approved