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A068908
Number of partitions of n modulo 5.
4
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.
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Mar 05 2002
STATUS
approved