login
A326357
a(n) = number of partitions of n that occur more than once among the condensed partitions of n; see A239312.
0
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 30 2019
EXTENSIONS
More terms from Alois P. Heinz, Jun 30 2019
STATUS
approved