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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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,tabl,easy

AUTHOR

Clark Kimberling, Jun 05 2019

STATUS

approved

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)