OFFSET
0,3
COMMENTS
A part x of a partition is neighborless if neither x - 1 nor x + 1 are parts.
EXAMPLE
The a(1) = 1 through a(8) = 9 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (111) (22) (41) (33) (52)
(31) (311) (42) (61)
(1111) (11111) (51) (331)
(222) (421)
(411) (511)
(3111) (4111)
(111111) (31111)
(1111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Function[ptn, Or@@Table[!MemberQ[ptn, x-1]&&!MemberQ[ptn, x+1], {x, Union[ptn]}]]]], {n, 0, 30}]
CROSSREFS
These partitions are ranked by the complement of A356736.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 24 2022
STATUS
approved