A240499 Number of partitions of n such that the multiplicity of the number of parts is a part.

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

Links

Table of n, a(n) for n=0..52.

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

Cf. A240496, A240497, A240498, A240500.

Sequence in context: A029602 A210041 A345280 * A248511 A210191 A110465

Adjacent sequences: A240496 A240497 A240498 * A240500 A240501 A240502

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved