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%I #22 Jul 14 2022 06:41:28
%S 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,
%T 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,
%U 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
%N Number of partitions of n modulo 7.
%C 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.
%H Henry Bottomley, <a href="http://www.se16.info/js/partitions.htm">Partition calculators using java applets</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = A010876(A000041(n)) = A068906(7, n).
%F 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]
%t Table[Mod[PartitionsP[n],7],{n,0,110}] (* _Harvey P. Dale_, Feb 17 2018 *)
%o (PARI) a(n) = numbpart(n) % 7; \\ _Michel Marcus_, Jul 14 2022
%Y Cf. A000041, A010876, A068906.
%Y Cf. A040051, A068907, A068908, A020919.
%K nonn
%O 0,3
%A _Henry Bottomley_, Mar 05 2002
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