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A114640
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Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal.
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29
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1, 1, 0, 0, 2, 1, 1, 0, 1, 1, 3, 2, 3, 3, 5, 0, 4, 5, 2, 3, 8, 6, 5, 10, 9, 9, 16, 14, 12, 16, 17, 10, 17, 15, 16, 19, 35, 17, 34, 37, 40, 31, 54, 36, 60, 61, 58, 63, 88, 58, 88, 87, 91, 84, 115, 93, 116, 108, 115, 130, 190, 143, 165, 214, 219, 200, 255, 240
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OFFSET
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0,5
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COMMENTS
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LINKS
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EXAMPLE
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The initial terms count the following integer partitions:
0: ()
1: (1)
4: (22)
4: (211)
5: (221)
6: (3111)
8: (41111)
9: (333)
10: (511111)
10: (3331)
10: (322111)
11: (332111)
11: (322211)
12: (6111111)
12: (4221111)
12: (33222)
13: (33322)
13: (333211)
13: (332221)
14: (71111111)
14: (52211111)
14: (4421111)
14: (4222211)
14: (333221)
(End)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Union[#]==Union[Length/@Split[#]]&]], {n, 0, 30}] (* Gus Wiseman, Apr 02 2019 *)
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CROSSREFS
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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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