OFFSET
0,4
EXAMPLE
The a(1) = 1 through a(9) = 6 partitions:
1 11 3 31 5 33 7 53 9
111 1111 311 3111 331 3311 333
11111 111111 31111 311111 531
1111111 11111111 33111
3111111
111111111
MATHEMATICA
nogapQ[m_]:=Or[m=={}, Union[m]==Range[Min[m], Max[m]]];
Table[Length[Select[IntegerPartitions[n], And@@OddQ/@#&&nogapQ[(#+1)/2]&]], {n, 0, 30}]
CROSSREFS
The initial case for compositions is A356604.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 03 2022
STATUS
approved