A240498 Number of partitions p of n such that the multiplicity of min(p)*max(p) is a part.

0, 1, 0, 1, 2, 4, 6, 8, 12, 17, 25, 35, 48, 65, 88, 116, 154, 203, 263, 342, 440, 562, 716, 908, 1141, 1436, 1794, 2234, 2771, 3431, 4223, 5194, 6359, 7770, 9462, 11502, 13929, 16852, 20318, 24458, 29364, 35204, 42088, 50257, 59865, 71212, 84531, 100208

Offset

0,5

Links

Table of n, a(n) for n=0..47.

Example

a(6) counts these 6 partitions:  51, 411, 3111, 21111, 321.

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, A240499, A240500.

Sequence in context: A241882 A238626 A168657 * A081954 A096903 A352107

Adjacent sequences: A240495 A240496 A240497 * A240499 A240500 A240501

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved