OFFSET
1,5
COMMENTS
All of these partitions have even length.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
EXAMPLE
The a(1) = 0 through a(10) = 10 partitions:
. (11) . (31) (32) (33) (52) (53) (54) (55)
(2111) (51) (2221) (71) (72) (73)
(2211) (4111) (3311) (3222) (91)
(3111) (5111) (6111) (3322)
(321111) (3331)
(4411)
(5311)
(7111)
(322111)
(421111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !IntegerQ[Median[Differences[Prepend[Reverse[#], 0]]]]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 22 2023
STATUS
approved