OFFSET
0,7
COMMENTS
We define a difference of a partition to be a difference of two adjacent parts.
EXAMPLE
The a(5) = 1 through a(10) = 17 partitions:
(311) (411) (511) (422) (522) (622)
(3111) (4111) (611) (711) (811)
(31111) (3311) (4221) (4222)
(4211) (4311) (4411)
(5111) (5211) (5221)
(41111) (6111) (5311)
(311111) (33111) (6211)
(42111) (7111)
(51111) (42211)
(411111) (43111)
(3111111) (52111)
(61111)
(331111)
(421111)
(511111)
(4111111)
(31111111)
MATHEMATICA
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[Length[Select[IntegerPartitions[n], (Min@@Differences[#]<-1)&&(Min@@Differences[conj[#]]<-1)&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 24 2022
STATUS
approved