OFFSET

0,2

LINKS

EXAMPLE

The a(1) = 1 through a(5) = 11 twice-partitions:

(1) (3) (5)

(21) (32)

(111) (41)

(1)(1)(1) (221)

(311)

(2111)

(11111)

(3)(1)(1)

(21)(1)(1)

(111)(1)(1)

(1)(1)(1)(1)(1)

MATHEMATICA

twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn], {ptn, IntegerPartitions[n]}];

Table[Length[Select[twiptn[n], OddQ[Length[#]]&&OddQ[Times@@Total/@#]&]], {n, 1, 15, 2}]

CROSSREFS

For odd parts instead of length and sums we have A270995.

Requiring odd lengths and odd parts gives A279374 aerated.

This is the case of A358824 with odd sums.

This is the odd-length case (hence odd bisection) of A358825.

For odd lengths (instead of length) we have A358827.

For odd lengths instead of sums we have A358834.

A000009 counts partitions into odd parts.

A027193 counts partitions of odd length.

A078408 counts odd-length partitions into odd parts.

A300301 aerated counts twice-partitions with odd sums and parts.

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 03 2022

STATUS

approved