A350636 - OEIS

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

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OFFSET

0,9

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.

FORMULA

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

CROSSREFS

Cf. A000726, A066447.

Sequence in context: A003879 A333885 A270060 * A078565 A211541 A026926

Adjacent sequences: A350633 A350634 A350635 * A350637 A350638 A350639

KEYWORD

nonn

AUTHOR

Michel Marcus, Jan 09 2022

STATUS

approved