A068909 - OEIS

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

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OFFSET

0,3

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

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

a(n) = Pm(n,1) with Pm(n,k) = if k<n then (Pm(n-k,k) + Pm(n,k+1)) mod 7 else 0^(n*(k-n)). [Reinhard Zumkeller, Jun 09 2009]

MATHEMATICA

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

PROG

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

CROSSREFS