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A356605
Number of integer compositions of n into odd parts covering an interval of odd positive integers.
3
1, 1, 1, 2, 3, 5, 6, 10, 15, 26, 41, 65, 104, 164, 262, 424, 687, 1112, 1792, 2898, 4677, 7556, 12197, 19699, 31836, 51466, 83234, 134593, 217674, 352057, 569452, 921165, 1490173, 2410784, 3900288, 6310436, 10210358, 16521108, 26733020, 43258086, 69999295
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}]
CROSSREFS
These compositions are ranked by the intersection of A060142 and A356841.
Before restricting to odds we have A107428, initial A107429.
The not necessarily gapless version is A324969 (essentially A000045).
The strict case is A332032.
The initial case is A356604.
The case of partitions is A356737, initial A053251 (ranked by A356232).
A000041 counts partitions, compositions A011782.
A066208 lists numbers with all odd prime indices, counted by A000009.
A073491 lists numbers with gapless prime indices, initial A055932.
Sequence in context: A018594 A018626 A018305 * A018693 A018255 A194358
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 31 2022
EXTENSIONS
More terms from Alois P. Heinz, Sep 01 2022
STATUS
approved