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A365922
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Number of non-subset-sums of strict integer partitions of n.
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10
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0, 1, 2, 4, 8, 11, 18, 25, 38, 51, 70, 93, 122, 159, 206, 263, 328, 420, 514, 645, 776, 967, 1154, 1413, 1686, 2042, 2414, 2890, 3394, 4062, 4732, 5598, 6494, 7652, 8836, 10329, 11884, 13833, 15830, 18376, 20936, 24131, 27476, 31547, 35780, 40966, 46292, 52737
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OFFSET
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1,3
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COMMENTS
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For an integer partition y of n, we call a positive integer k <= n a non-subset-sum iff there is no submultiset of y summing to k.
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LINKS
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EXAMPLE
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The a(6) = 11 ways, showing each strict partition and its non-subset-sums:
(6): 1,2,3,4,5
(51): 2,3,4
(42): 1,3,5
(321):
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MATHEMATICA
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Table[Total[Length[Complement[Range[n], Total/@Subsets[#]]]& /@ Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 30}]
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CROSSREFS
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The zero-full complement (subset-sums) is A365925, non-strict A304792.
A364350 counts combination-free strict partitions, complement A364839.
A365543 counts partitions with a submultiset summing to k.
A365661 counts strict partitions w/ a subset summing to k.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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