A068909 Number of partitions of n modulo 7.

1, 1, 2, 3, 5, 0, 4, 1, 1, 2, 0, 0, 0, 3, 2, 1, 0, 3, 0, 0, 4, 1, 1, 2, 0, 5, 0, 0, 1, 1, 4, 3, 5, 0, 4, 1, 1, 0, 3, 0, 0, 0, 2, 2, 2, 3, 5, 0, 0, 2, 1, 4, 0, 0, 0, 0, 3, 2, 2, 3, 5, 0, 4, 2, 2, 2, 3, 5, 0, 4, 3, 2, 4, 6, 5, 0, 0, 2, 2, 4, 3, 5, 0, 0, 3, 3, 6, 6, 3, 0, 1, 3, 3, 4, 3, 5, 0, 0, 4, 3, 4, 6, 5, 0, 1

Offset: 0

Author

Henry Bottomley, Mar 05 2002

Keywords

• nonn

Comments

Of the partitions of numbers from 1 to 100000: 27193 are 0, 12078 are 1, 12203 are 2, 12260 are 3, 12231 are 4, 12003 are 5 and 12032 are 6 modulo 7, largely because the number of partitions of 7m+5 is always a multiple of 7.

Links

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

Crossrefs

Cf. A000041, A010876, A068906.

Cf. A040051, A068907, A068908, A020919.

Programs

Mathematica

Table[Mod[PartitionsP[n],7],{n,0,110}] (* Harvey P. Dale, Feb 17 2018 *)

PARI

a(n) = numbpart(n) % 7; \\ Michel Marcus, Jul 14 2022

Formula

a(n) = A010876(A000041(n)) = A068906(7, n).

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