A240539 Number of partitions p of n such that the m(M(p)) is a part, where m = multiplicity, M = the minimum multiplicity of the parts of p.

0, 1, 0, 1, 3, 2, 4, 6, 8, 11, 17, 20, 30, 39, 54, 66, 94, 114, 150, 192, 249, 305, 402, 492, 624, 776, 974, 1187, 1495, 1820, 2247, 2745, 3368, 4065, 4987, 6007, 7274, 8769, 10576, 12648, 15222, 18172, 21695, 25866, 30789, 36488, 43349, 51267, 60550, 71491

Offset

0,5

Links

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

Example

a(6) counts these partitions:  51, 321, 3111, 2211; e.g., the multiplicies of the parts of p = {3111} and 1 and 3, of which the min is 1, and the multiplicity of 1 in p is 3, 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. A240538.

Sequence in context: A195208 A114651 A340064 * A138245 A163328 A164109

Adjacent sequences: A240536 A240537 A240538 * A240540 A240541 A240542

Keyword

nonn,easy

Author

Clark Kimberling, Apr 07 2014

Status

approved