A356737 - OEIS

A356737

Number of integer partitions of n into odd parts covering an interval of odd numbers.

1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 7, 8, 9, 10, 13, 13, 15, 17, 19, 21, 25, 26, 29, 33, 37, 40, 46, 49, 54, 61, 66, 72, 81, 87, 97, 106, 115, 125, 139, 150, 163, 179, 193, 210, 232, 248, 269, 293, 317, 343, 373, 401, 433, 470, 507, 545, 590, 633, 682, 737, 790

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..61.

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 strict case is A034178, for compositions A332032.

The initial case is A053251, ranked by A356232 and A356603.

The initial case for compositions is A356604.

The version for compositions is A356605, ranked by A060142 /\ A356841.

A000041 counts partitions, compositions A011782.

A066208 lists numbers with all odd prime indices, counted by A000009.

A073491 lists gapless numbers, initial A055932.

Cf. A001227, A066205, A107428, A107429, A333217, A356224, A356846.

Sequence in context: A317908 A056039 A181972 * A058747 A034322 A362612

Adjacent sequences: A356734 A356735 A356736 * A356738 A356739 A356740

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 03 2022

STATUS

approved