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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
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
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
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Jun 05 2019
STATUS
approved