A241518 Number of partitions p of n such that #m(1) = #m(2), where #m(i) = number of numbers in p that have multiplicity i.

1, 0, 0, 1, 2, 3, 3, 4, 5, 6, 8, 12, 16, 23, 27, 41, 46, 63, 71, 96, 109, 148, 161, 219, 256, 332, 379, 500, 580, 738, 859, 1079, 1250, 1560, 1791, 2220, 2563, 3116, 3595, 4369, 5054, 6080, 7020, 8418, 9729, 11617, 13409, 15911, 18417, 21713, 25078, 29467

Offset

0,5

Links

Table of n, a(n) for n=0..51.

Example

a(6) counts these 3 partitions:  411, 222, 111111.

Mathematica

z = 30; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; v[p_] :=  Length[DeleteDuplicates[Select[p, Count[p, #] == 2 &]]]; Table[Count[IntegerPartitions[n], p_ /; u[p] == v[p]], {n, 0, z}]

Crossrefs

Cf. A241274.

Sequence in context: A205216 A304885 A017853 * A125616 A367220 A141472

Adjacent sequences: A241515 A241516 A241517 * A241519 A241520 A241521

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved