OFFSET
0,9
COMMENTS
EXAMPLE
The a(6) = 1 through a(11) = 16 partitions:
(321) (3211) (431) (531) (541) (641)
(521) (3321) (721) (731)
(3221) (4311) (4321) (4331)
(32111) (5211) (5221) (5321)
(32211) (5311) (5411)
(321111) (32221) (7211)
(33211) (33221)
(43111) (43211)
(52111) (52211)
(322111) (53111)
(3211111) (322211)
(332111)
(431111)
(521111)
(3221111)
(32111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], #=={}||And@@IntegerQ/@(#/Min@@#)&&!And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
CROSSREFS
The first condition alone gives A083710.
The Heinz numbers of these partitions are 1 and A343340.
The second condition alone gives A343341.
The opposite version is A343344.
The strict case is A343381.
A000009 counts strict partitions.
A000041 counts partitions.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 15 2021
STATUS
approved