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