A325772 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

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)?

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A006128, A325771, A325773, A325774.

Sequence in context: A208648 A005131 A105477 * A226174 A208482 A199856

Adjacent sequences: A325769 A325770 A325771 * A325773 A325774 A325775

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Jun 05 2019

STATUS

approved