A350636 a(n) is the number of partitions of n in which no part is divisible by 3 minus the number of basis partitions of n.

0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 6, 7, 10, 12, 17, 20, 28, 34, 45, 55, 72, 87, 111, 133, 167, 200, 247, 295, 362, 431, 523, 621, 749, 885, 1059, 1247, 1482, 1739, 2055, 2402, 2826, 3293, 3855, 4479, 5225, 6051, 7032, 8123, 9406, 10837, 12509, 14372, 16541, 18960, 21756, 24880, 28477

Offset: 0

Author

Michel Marcus, Jan 09 2022

Keywords

• nonn

Comments

Andrews conjectures that a(n)>0 for n>3.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• George E. Andrews, Partition Identities for Two-Color Partitions, Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Special Commemorative volume in honour of Srinivasa Ramanujan, 2021, 44, pp.74-80. hal-03498190. See p. 79.

Crossrefs

Cf. A000726, A066447.

Formula

a(n) = A000726(n) - A066447(n).