OFFSET
0,4
EXAMPLE
The a(1) = 1 through a(8) = 15 compositions:
(1) (11) (3) (13) (5) (33) (7) (35)
(111) (31) (113) (1113) (133) (53)
(1111) (131) (1131) (313) (1133)
(311) (1311) (331) (1313)
(11111) (3111) (11113) (1331)
(111111) (11131) (3113)
(11311) (3131)
(13111) (3311)
(31111) (111113)
(1111111) (111131)
(111311)
(113111)
(131111)
(311111)
(11111111)
MATHEMATICA
nogapQ[m_]:=m=={}||Union[m]==Range[Min[m], Max[m]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], And@@OddQ/@#&&nogapQ[(#+1)/2]&]], {n, 0, 15}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 31 2022
EXTENSIONS
More terms from Alois P. Heinz, Sep 01 2022
STATUS
approved