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

0,3

Comments

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

Links

Table of n, a(n) for n=0..104.

Henry Bottomley, Partition calculators using java applets

Index entries for sequences related to partitions

Formula

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

a(n) = Pm(n,1) with Pm(n,k) = if k<n then (Pm(n-k,k) + Pm(n,k+1)) mod 3 else 0^(n*(k-n)). - Reinhard Zumkeller, Jun 09 2009

Mathematica

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

Prog

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

Crossrefs

Cf. A040051, A068908, A068909, A020919.

Sequence in context: A127543 A353237 A280830 * A219762 A227696 A033687

Adjacent sequences: A068904 A068905 A068906 * A068908 A068909 A068910

Keyword

nonn

Author

Henry Bottomley, Mar 05 2002

Status

approved