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A367213
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Number of integer partitions of n whose length (number of parts) is not equal to the sum of any submultiset.
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25
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0, 0, 1, 1, 2, 2, 5, 4, 7, 8, 12, 13, 19, 21, 29, 33, 45, 49, 67, 73, 97, 108, 139, 152, 196, 217, 274, 303, 379, 420, 523, 579, 709, 786, 960, 1061, 1285, 1423, 1714, 1885, 2265, 2498, 2966, 3280, 3881, 4268, 5049, 5548, 6507, 7170, 8391, 9194, 10744, 11778, 13677
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OFFSET
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0,5
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COMMENTS
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These partitions are necessarily incomplete (A365924).
Are there any decreases after the initial terms?
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LINKS
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EXAMPLE
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The a(3) = 1 through a(9) = 8 partitions:
(3) (4) (5) (6) (7) (8) (9)
(3,1) (4,1) (3,3) (4,3) (4,4) (5,4)
(5,1) (6,1) (5,3) (6,3)
(2,2,2) (5,1,1) (7,1) (8,1)
(4,1,1) (4,2,2) (4,4,1)
(6,1,1) (5,2,2)
(5,1,1,1) (7,1,1)
(6,1,1,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], FreeQ[Total/@Subsets[#], Length[#]]&]], {n, 0, 10}]
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CROSSREFS
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The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum or linear combination of the parts. The current sequence is starred.
sum-full sum-free comb-full comb-free
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Triangles:
A046663 counts partitions of n without a subset-sum k, strict A365663.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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