
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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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(nk,k) + Pm(n,k+1)) mod 7 else 0^(n*(kn)). [From Reinhard Zumkeller, Jun 09 2009]


MATHEMATICA

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


CROSSREFS

Cf. A040051, A068907, A068908, A020919.
Sequence in context: A118308 A284214 A174548 * A039705 A254271 A082118
Adjacent sequences: A068906 A068907 A068908 * A068910 A068911 A068912


KEYWORD

nonn


AUTHOR

Henry Bottomley, Mar 05 2002


STATUS

approved

