A241090 Number of partitions p of n such that (number of numbers in p having multiplicity > 1) = number of 1s in p.

1, 0, 1, 1, 1, 3, 3, 5, 6, 10, 12, 16, 21, 29, 36, 47, 58, 77, 93, 121, 146, 185, 225, 280, 338, 419, 505, 612, 743, 888, 1075, 1283, 1539, 1822, 2190, 2575, 3073, 3612, 4287, 5022, 5936, 6938, 8158, 9527, 11151, 12983, 15156, 17617, 20468, 23770, 27531

Offset

0,6

Links

Table of n, a(n) for n=0..50.

Example

a(6) counts these 3 partitions:  6, 42, 2211.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; Table[Count[f[n], p_ /; e[p] == Count[p, 1]], {n, 0, z}]

Crossrefs

Cf. A241409, A241131.

Sequence in context: A048274 A351012 A059892 * A091607 A276434 A183561

Adjacent sequences: A241087 A241088 A241089 * A241091 A241092 A241093

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved