A357456 Number of partitions of n into two or more odd parts.

0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 15, 17, 22, 26, 32, 37, 46, 53, 64, 75, 89, 103, 122, 141, 165, 191, 222, 255, 296, 339, 390, 447, 512, 584, 668, 759, 864, 981, 1113, 1259, 1426, 1609, 1816, 2047, 2304, 2589, 2910, 3263, 3658, 4096, 4582, 5119, 5718, 6377, 7108

Offset: 0

Author

Ilya Gutkovskiy, Sep 29 2022

Keywords

• nonn

Links

• Harmandeep Kaur and Muhammad Asif Rana, Partitions with unique largest part and their generating functions, arXiv:2506.11447 [math.CO], 2025. See p. 6.

Crossrefs

Cf. A000009, A000035, A111133, A357457.

Programs

Mathematica

Table[Count[IntegerPartitions[n], ?(And[Length[#] > 1, AllTrue[#, OddQ]] &)], {n, 0, 56}] (* _Michael De Vlieger, Jun 23 2025 *)

Formula

a(n) = A000009(n) - A000035(n) for n > 0.