A240538 Number of partitions p of n such that the m(M(p)) is a part, where m = multiplicity, M = the maximum multiplicity of the parts of p.

0, 1, 0, 1, 3, 2, 4, 4, 8, 9, 17, 19, 26, 32, 47, 54, 81, 96, 126, 161, 210, 249, 331, 407, 514, 630, 794, 962, 1206, 1467, 1803, 2197, 2694, 3235, 3961, 4761, 5762, 6914, 8338, 9951, 11954, 14232, 16990, 20188, 24028, 28407, 33713, 39786, 46996, 55329

Offset

0,5

Links

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

Example

a(6) counts these 4 partitions: 51, 321, 3111, 2211; e.g., the multiplicities of the parts of p = {2,2,1,1} are 2 and 2, of which the max is 2, and the multiplicity of 2 in p is 2, which is a part of p.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; m1[p_] := Max[Map[Length, Split[p]]]; m2[p_] := Min[Map[Length, Split[p]]];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, m1[p]]]], {n, 0, z}]  (* A240538 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, m2[p]]]], {n, 0, z}]  (* A240539 *)

Crossrefs

Cf. A240539.

Sequence in context: A309511 A195472 A370806 * A326923 A365613 A338315

Adjacent sequences: A240535 A240536 A240537 * A240539 A240540 A240541

Keyword

nonn,easy

Author

Clark Kimberling, Apr 07 2014

Status

approved