A068908 Number of partitions of n modulo 5.

1, 1, 2, 3, 0, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 3, 1, 0, 3, 0, 4, 2, 4, 3, 0, 3, 2, 2, 0, 0, 3, 3, 4, 1, 0, 4, 3, 4, 3, 0, 1, 3, 4, 1, 0, 1, 3, 4, 0, 0, 2, 0, 1, 4, 0, 3, 0, 4, 0, 0, 3, 0, 3, 4, 0, 4, 1, 3, 4, 0, 1, 2, 0, 4, 0, 2, 2, 3, 4, 0, 3, 4, 2, 2, 0, 4, 4, 0, 1, 0, 2, 1, 4, 0, 0

Offset: 0

Author

Henry Bottomley, Mar 05 2002

Keywords

• nonn

Comments

Of the partitions of numbers from 1 to 100000: 36256 are 0, 15758 are 1, 16133 are 2, 16028 are 3 and 15825 are 4 modulo 5, largely because the number of partitions of 5m+4 is always a multiple of 5.

Links

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

Crossrefs

Cf. A000041, A010874, A068906.

Cf. A040051, A068907, A068909, A020919.

Programs

Mathematica

Mod[PartitionsP[Range[0,110]],5] (* Harvey P. Dale, Dec 20 2023 *)

PARI

a(n) = numbpart(n) % 5; \\ Michel Marcus, Jul 14 2022

Formula

a(n) = A010874(A000041(n)) = A068906(5, n).

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