A240493 Number of partitions of n such that the multiplicity of the least part is a part.

0, 1, 0, 1, 3, 2, 4, 6, 9, 13, 18, 21, 34, 42, 58, 74, 104, 124, 171, 210, 278, 346, 448, 546, 711, 866, 1094, 1338, 1684, 2036, 2546, 3074, 3798, 4583, 5618, 6741, 8237, 9848, 11927, 14246, 17177, 20418, 24516, 29067, 34719, 41078, 48856, 57605, 68310

Offset

0,5

Links

Table of n, a(n) for n=0..48.

Example

a(6) counts these 4 partitions:  51, 321, 3111, 2211.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Mean[p]]]], {n, 0, z}]  (* A240491 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Median[p]]]], {n, 0, z}]  (* A240492 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]]]], {n, 0, z}]  (* A240493 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p]]]], {n, 0, z}]  (* A240494 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p] - Min[p]]]], {n, 0, z}]  (* A240495 *)

Crossrefs

Cf. A240491 - A240495.

Sequence in context: A164109 A116425 A019653 * A095258 A114745 A352915

Adjacent sequences: A240490 A240491 A240492 * A240494 A240495 A240496

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved