A240500 Number of partitions of n such that the multiplicity of 2*(number of parts) is a part.

0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 2, 2, 5, 5, 6, 9, 9, 13, 17, 21, 25, 32, 39, 48, 59, 73, 87, 109, 129, 156, 190, 226, 271, 328, 388, 463, 552, 654, 772, 919, 1078, 1271, 1500, 1760, 2059, 2418, 2820, 3296, 3844, 4475, 5198, 6048, 7006, 8121, 9400, 10866

Offset

0,12

Links

Table of n, a(n) for n=0..57.

Example

a(14) counts these 5 partitions:  [10,1111, [8,4,1,1], [8,3,2,1], [7,6,1], [6,6,2].

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, A240499.

Sequence in context: A035643 A324925 A163946 * A344264 A308512 A308857

Adjacent sequences: A240497 A240498 A240499 * A240501 A240502 A240503

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved