OFFSET
1,2
COMMENTS
Also the number of integer partitions of n with a unique middle part. This means that either the length is odd or the two middle parts are equal. For example, the partition (4,3,2,1) has middle parts {2,3} so is not counted under a(10), but (3,2,2,1) has middle parts {2,2} so is counted under a(8). - Gus Wiseman, May 13 2023
FORMULA
For all n, a(n) >= A027193(n) (because when a partition of n has an odd number of parts, its median is simply the part at the middle). - Antti Karttunen, Feb 27 2014
EXAMPLE
a(6) counts these partitions: 6, 411, 33, 321, 3111, 222, 21111, 111111.
MATHEMATICA
Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Median[p]]], {n, 40}]
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 27 2014
STATUS
approved