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A325771 Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 2), for k = 0, 1.

%I A325771 #11 Feb 02 2023 13:23:36
%S A325771 0,1,1,2,1,5,4,8,5,15,11,24,15,39,28,58,38,90,62,130,85,190,131,268,
%T A325771 177,379,258,522,346,722,489,974,648,1317,890,1754,1168,2330,1572,
%U A325771 3058,2042,4010,2699,5200,3475,6731,4532,8642,5783,11068,7446,14076,9430
%N A325771 Rectangular array:  row n shows the number of parts in all partitions of n that are == k (mod 2), for k = 0, 1.
%C A325771 Row n partitions A006128 into 2 parts, r(n,0) + r(n,1) = p(n) = A006128(n).  What is the limiting behavior of r(n,0)/p(n)?
%H A325771 Clark Kimberling, <a href="/A325771/b325771.txt">Table of n, a(n) for n = 1..100</a>
%F A325771 (row n) = (A066898(n), A066897(n)).
%e A325771 First 15 rows:
%e A325771     0    1
%e A325771     1    2
%e A325771     1    5
%e A325771     4    8
%e A325771     5   15
%e A325771    11   24
%e A325771    15   39
%e A325771    28   58
%e A325771    38   90
%e A325771    62  130
%e A325771    85  190
%e A325771   131  268
%e A325771   177  379
%e A325771   258  522
%e A325771   346  722
%t A325771 f[n_] := Mod[Flatten[IntegerPartitions[n]], 2];
%t A325771 Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1}]  (* A325771 array *)
%t A325771 Flatten[%] (* A325771 sequence *)
%Y A325771 Cf. A006128, A066898, A066897, A325772, A325773, A325774.
%K A325771 nonn,tabf,easy
%O A325771 1,4
%A A325771 _Clark Kimberling_, Jun 05 2019