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A325772 Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 3), for k = 0, 1, 2.

%I A325772 #12 Aug 17 2020 13:42:14
%S A325772 0,1,0,0,2,1,1,4,1,1,8,3,2,13,5,5,21,9,7,34,13,11,52,23,19,77,32,27,
%T A325772 114,51,40,163,72,61,232,106,85,325,146,120,450,210,170,614,284,232,
%U A325772 836,395,316,1120,529,433,1494,717,576,1976,946,767,2599,1264
%N A325772 Rectangular array:  row n shows the number of parts in all partitions of n that are == k (mod 3), for k = 0, 1, 2.
%C A325772 Row n partitions A006128 into 3 parts, r(n,0) + r(n,1) + r(n,2) = p(n) = A006128(n).  What is the limiting behavior of r(n,0)/p(n)?
%H A325772 Clark Kimberling, <a href="/A325772/b325772.txt">Table of n, a(n) for n = 1..150</a>
%e A325772 First 15 rows:
%e A325772     0     1     0
%e A325772     0     2     1
%e A325772     1     4     1
%e A325772     1     8     3
%e A325772     2    13     5
%e A325772     5    21     9
%e A325772     7    34    13
%e A325772    11    52    23
%e A325772    19    77    32
%e A325772    27   114    51
%e A325772    40   163    72
%e A325772    61   232   106
%e A325772    85   325   146
%e A325772   120   450   210
%e A325772   170   614   264
%t A325772 f[n_] := Mod[Flatten[IntegerPartitions[n]], 3];
%t A325772 Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1,2}]  (* A325772 array *)
%t A325772 Flatten[%] (* A325772 sequence *)
%Y A325772 Cf. A006128, A325771, A325773, A325774.
%K A325772 nonn,tabf,easy
%O A325772 1,5
%A A325772 _Clark Kimberling_, Jun 05 2019