A240496 Number of partitions p of n such that the multiplicity of 2*min(p) is a part.

0, 0, 0, 1, 1, 2, 3, 4, 6, 9, 14, 18, 25, 35, 46, 62, 83, 109, 142, 185, 238, 305, 390, 494, 624, 787, 984, 1227, 1528, 1892, 2334, 2876, 3527, 4313, 5267, 6406, 7773, 9416, 11371, 13701, 16481, 19774, 23678, 28305, 33761, 40198, 47789, 56700, 67159, 79438

Offset

0,6

Links

Table of n, a(n) for n=0..49.

Example

a(9) counts these 9 partitions:  621, 5211, 4221, 42111, 3321, 32211, 321111, 2211111, 21111111.

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. A240497, A240498, A240499, A240500.

Sequence in context: A220126 A328071 A039884 * A212464 A302016 A078620

Adjacent sequences: A240493 A240494 A240495 * A240497 A240498 A240499

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved