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

0,5

Links

Table of n, a(n) for n=0..56.

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

Formula

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

Mathematica

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

Crossrefs

Cf. A000009, A000035, A111133, A357457.

Sequence in context: A161254 A241313 A241317 * A185224 A001996 A317084

Adjacent sequences: A357453 A357454 A357455 * A357457 A357458 A357459

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 29 2022

Status

approved