A326357 a(n) = number of partitions of n that occur more than once among the condensed partitions of n; see A239312.

0, 0, 1, 1, 1, 3, 2, 4, 5, 7, 11, 11, 15, 19, 25, 29, 39, 47, 61, 67, 85, 107, 128, 154, 182, 219, 264, 310, 366, 441, 514, 608, 705, 836, 974, 1128, 1312, 1530, 1776, 2053, 2367, 2735, 3156, 3598, 4145, 4745, 5463, 6204, 7084, 8068, 9241, 10455, 11906, 13488

Offset

0,6

Links

Table of n, a(n) for n=0..53.

Example

The partitions of 5 are [5], [4,1], [3,2], [3,1,1], [2,2,1], [2,1,1,1], [1,1,1,1,1], with respective condensations [5], [4,1], [3,2], [3,2], [4,1], [3,2], [5]; of these, three occur more than once, so that a(5) = 3.

Mathematica

p[n_] := IntegerPartitions[n];
m[n_] := Map[Split, p[n]];
t[n_, k_] := Map[Total, m[n][[k]]];
u[n_] := Table[Sort[t[n, k], Greater], {k, 1, Length[p[n]]}]
v[n_] := Tally[u[n]];
w[n_] := Length[Select[v[n], #[[2]] > 1 &] ]; l
Table[w[n], {n, 1, 20}]

Crossrefs

Cf. A000009, A000041, A239312.

Sequence in context: A125060 A039882 A370803 * A354731 A164287 A086962

Adjacent sequences: A326354 A326355 A326356 * A326358 A326359 A326360

Keyword

nonn,easy

Author

Clark Kimberling, Jun 30 2019

Extensions

More terms from Alois P. Heinz, Jun 30 2019

Status

approved