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

0, 1, 1, 2, 1, 5, 4, 8, 5, 15, 11, 24, 15, 39, 28, 58, 38, 90, 62, 130, 85, 190, 131, 268, 177, 379, 258, 522, 346, 722, 489, 974, 648, 1317, 890, 1754, 1168, 2330, 1572, 3058, 2042, 4010, 2699, 5200, 3475, 6731, 4532, 8642, 5783, 11068, 7446, 14076, 9430

Offset

1,4

Comments

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)?

Links

Clark Kimberling, Table of n, a(n) for n = 1..100

Formula

(row n) = (A066898(n), A066897(n)).

Example

First 15 rows:
    0    1
    1    2
    1    5
    4    8
    5   15
   11   24
   15   39
   28   58
   38   90
   62  130
   85  190
  131  268
  177  379
  258  522
  346  722

Mathematica

f[n_] := Mod[Flatten[IntegerPartitions[n]], 2];
Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1}]  (* A325771 array *)
Flatten[%] (* A325771 sequence *)

Crossrefs

Cf. A006128, A066898, A066897, A325772, A325773, A325774.

Sequence in context: A171175 A176053 A259791 * A207480 A166517 A019473

Adjacent sequences: A325768 A325769 A325770 * A325772 A325773 A325774

Keyword

nonn,tabf,easy

Author

Clark Kimberling, Jun 05 2019

Status

approved