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

0,3

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

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

a(n) = Pm(n,1) with Pm(n,k) = if k<n then (Pm(n-k,k) + Pm(n,k+1)) mod 5 else 0^(n*(k-n)). [Reinhard Zumkeller, Jun 09 2009]

Mathematica

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

Prog

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

Crossrefs

Cf. A000041, A010874, A068906.

Cf. A040051, A068907, A068909, A020919.

Sequence in context: A336207 A344909 A126832 * A226192 A113407 A039703

Adjacent sequences: A068905 A068906 A068907 * A068909 A068910 A068911

Keyword

nonn

Author

Henry Bottomley, Mar 05 2002

Status

approved