cp's OEIS Frontend

A325773 Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 4), for k = 0, 1, 2, 3.

%I A325773 #10 Feb 02 2023 13:25:15
%S A325773 0,1,0,0,0,2,1,0,0,4,1,1,1,7,3,1,1,13,4,2,2,20,9,4,3,32,12,7,7,48,21,
%T A325773 10,9,73,29,17,15,106,47,24,21,153,64,37,34,215,97,53,46,303,131,76,
%U A325773 68,416,190,106,92,571,254,151,134,770,355,204,178,1037
%N A325773 Rectangular array:  row n shows the number of parts in all partitions of n that are == k (mod 4), for k = 0, 1, 2, 3.
%C A325773 Row n partitions A006128 into 4 parts, r(n,0) + r(n,1) + r(n,3) + r(n,4) = p(n) = A006128(n).  What is the limiting behavior of r(n,0)/p(n)?
%H A325773 Clark Kimberling, <a href="/A325773/b325773.txt">Table of n, a(n) for n = 1..200</a>
%e A325773 First 15 rows:
%e A325773    0      1      0      0
%e A325773    0      2      1      0
%e A325773    0      4      1      1
%e A325773    1      7      3      1
%e A325773    1     13      4      2
%e A325773    2     20      9      4
%e A325773    3     32     12      7
%e A325773    7     48     21     10
%e A325773    9     73     29     17
%e A325773   15    106     47     24
%e A325773   21    153     64     37
%e A325773   34    215     97     53
%e A325773   46    303    131     76
%e A325773   68    416    190    106
%e A325773   92    571    254    151
%t A325773 f[n_] := Mod[Flatten[IntegerPartitions[n]], 4];
%t A325773 Table[Count[f[n], k], {n, 1, 40}, {k,0,1,2,3}]  (* A325773 array *)
%t A325773 Flatten[%] (* A325773 sequence *)
%Y A325773 Cf. A006128, A325771, A325772, A325774.
%K A325773 nonn,tabf,easy
%O A325773 1,6
%A A325773 _Clark Kimberling_, Jun 05 2019