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.

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, 114, 51, 40, 163, 72, 61, 232, 106, 85, 325, 146, 120, 450, 210, 170, 614, 284, 232, 836, 395, 316, 1120, 529, 433, 1494, 717, 576, 1976, 946, 767, 2599, 1264

Offset: 1

Author

Clark Kimberling, Jun 05 2019

Keywords

• nonn
• tabf
• easy

Comments

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)?

Examples

			First 15 rows:
    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   114    51
   40   163    72
   61   232   106
   85   325   146
  120   450   210
  170   614   264
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A006128, A325771, A325773, A325774.

Programs

Mathematica

f[n_] := Mod[Flatten[IntegerPartitions[n]], 3];
Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1,2}]  (* A325772 array *)
Flatten[%] (* A325772 sequence *)