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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

%I

%S 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,

%T 12,6,3,3,47,20,10,6,5,70,28,16,9,9,102,44,23,14,13,147,61,34,20,19,

%U 208,91,50,31,28,290,124,71,43,40,400,178,99,63,58,546

%N 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.

%C 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)?

%H Clark Kimberling, <a href="/A325774/b325774.txt">Table of n, a(n) for n = 1..250</a>

%e First 15 rows:

%e 0 1 0 0 0

%e 0 2 1 0 0

%e 0 4 1 1 0

%e 0 7 3 1 1

%e 1 12 4 2 1

%e 1 20 8 4 2

%e 2 31 12 6 3

%e 3 47 20 10 6

%e 5 70 28 16 9

%e 9 102 44 23 14

%e 13 147 61 34 20

%e 19 208 91 50 31

%e 28 290 124 71 43

%e 40 400 178 99 63

%e 58 546 239 139 86

%t f[n_] := Mod[Flatten[IntegerPartitions[n]], 5];

%t Table[Count[f[n], k], {n, 1, 40}, {k,0,1,2,3,4}] (* A325774 array *)

%t Flatten[%] (* A325773 sequence *)

%Y Cf. A006128, A325771, A325772, A325773.

%K nonn,tabl,easy

%O 1,7

%A _Clark Kimberling_, Jun 05 2019

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Last modified October 1 02:38 EDT 2022. Contains 357134 sequences. (Running on oeis4.)