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A240499
Number of partitions of n such that the multiplicity of the number of parts is a part.
5
0, 1, 0, 1, 1, 1, 1, 1, 3, 5, 3, 7, 8, 11, 13, 21, 24, 33, 39, 52, 65, 85, 100, 132, 161, 203, 245, 310, 369, 464, 556, 685, 823, 1008, 1198, 1465, 1745, 2103, 2501, 3009, 3557, 4261, 5031, 5987, 7058, 8370, 9823, 11613, 13611, 16014, 18725, 21974, 25615
OFFSET
0,9
EXAMPLE
a(9) counts these 5 partitions: 531, 51111, 4311, 4221, 333.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Min[p]]]], {n, 0, z}] (* A240496 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, (Min[p] + Max[p])/2]]], {n, 1, z}] (* A240497 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]*Max[p]]]], {n, 0, z}] (* A240498 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Length[p]]]], {n, 0, z}] (* A240499 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Length[p]]]], {n, 0, z}] (* A240500 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 06 2014
STATUS
approved