login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A068909 Number of partitions of n modulo 7. 3
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
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
Sequence in context: A371224 A284214 A174548 * A039705 A254271 A082118
KEYWORD
nonn
AUTHOR
Henry Bottomley, Mar 05 2002
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)