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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. 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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)?

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A006128, A325771, A325772, A325773.

Sequence in context: A036868 A326453 A130116 * A350488 A212868 A184616

Adjacent sequences:  A325771 A325772 A325773 * A325775 A325776 A325777

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Jun 05 2019

STATUS

approved

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Last modified August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)