A068907 Number of partitions of n modulo 3.

1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 1, 2, 2, 2, 0, 2, 0, 0, 1, 1, 2, 0, 2, 1, 2, 2, 0, 1, 1, 2, 2, 2, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1, 2, 0, 2, 0

Offset: 0

Author

Henry Bottomley, Mar 05 2002

Keywords

• nonn

Comments

Of the partitions of numbers from 1 to 100000: 33344 are 0, 33193 are 1 and 33463 are 2 modulo 3.

Links

• Henry Bottomley, Partition calculators using java applets
• Index entries for sequences related to partitions

Crossrefs

Cf. A040051, A068908, A068909, A020919.

Programs

Mathematica

Table[ Mod[ PartitionsP@ n, 3], {n, 105}] (* Robert G. Wilson v, Mar 25 2011 *)

PARI

a(n) = numbpart(n) % 3; \\ Michel Marcus, Jul 14 2022

Formula

a(n) = A010872(A000041(n)) = A068906(3, n)

a(n) = Pm(n,1) with Pm(n,k) = if kReinhard Zumkeller, Jun 09 2009