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A114640 Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal. 29
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
The Heinz numbers of these partitions are given by A109297. - Gus Wiseman, Apr 02 2019
LINKS
EXAMPLE
From Gus Wiseman, Apr 02 2019: (Start)
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)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Union[#]==Union[Length/@Split[#]]&]], {n, 0, 30}] (* Gus Wiseman, Apr 02 2019 *)
CROSSREFS
Sequence in context: A209354 A294446 A318163 * A056890 A321519 A346392
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 18 2006
EXTENSIONS
More terms from Alois P. Heinz, Aug 09 2016
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)