OFFSET

0,4

COMMENTS

For each partition of n, let

d = number of terms that are not repeated;

r = number of terms that are repeated.

a(n) is the number of partitions such that d > r.

Also the number of integer partitions of n with median multiplicity 1. - Gus Wiseman, Mar 20 2023

EXAMPLE

The partitions of 6 are 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111.

These have d > r: 6, 51, 42, 321

These have d = r: 411, 3222, 21111

These have d < r: 33, 222, 2211, 111111

Thus, a(6) = 4.

MATHEMATICA

z = 30; d[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]];

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

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 03 2020

STATUS

approved