A325774 Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 5), for k = 0, 1, 2, 3, 4.

0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 4, 1, 1, 0, 0, 7, 3, 1, 1, 1, 12, 4, 2, 1, 1, 20, 8, 4, 2, 2, 31, 12, 6, 3, 3, 47, 20, 10, 6, 5, 70, 28, 16, 9, 9, 102, 44, 23, 14, 13, 147, 61, 34, 20, 19, 208, 91, 50, 31, 28, 290, 124, 71, 43, 40, 400, 178, 99, 63, 58, 546

Offset: 1

Author

Clark Kimberling, Jun 05 2019

Keywords

• nonn
• tabf
• easy

Comments

Row n partitions A006128 into 5 parts, r(n,0) + r(n,1) + r(n,3) + r(n,4) + r(n,5) = p(n) = A006128(n). What is the limiting behavior of r(n,0)/p(n)?

Examples

			First 15 rows:
   0     1     0     0     0
   0     2     1     0     0
   0     4     1     1     0
   0     7     3     1     1
   1    12     4     2     1
   1    20     8     4     2
   2    31    12     6     3
   3    47    20    10     6
   5    70    28    16     9
   9   102    44    23    14
  13   147    61    34    20
  19   208    91    50    31
  28   290   124    71    43
  40   400   178    99    63
  58   546   239   139    86
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A006128, A325771, A325772, A325773.

Programs

Mathematica

f[n_] := Mod[Flatten[IntegerPartitions[n]], 5];
Table[Count[f[n], k], {n, 1, 40}, {k,0,1,2,3,4}]  (* A325774 array *)
Flatten[%] (* A325773 sequence *)