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A325773
Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 4), for k = 0, 1, 2, 3.
4
0, 1, 0, 0, 0, 2, 1, 0, 0, 4, 1, 1, 1, 7, 3, 1, 1, 13, 4, 2, 2, 20, 9, 4, 3, 32, 12, 7, 7, 48, 21, 10, 9, 73, 29, 17, 15, 106, 47, 24, 21, 153, 64, 37, 34, 215, 97, 53, 46, 303, 131, 76, 68, 416, 190, 106, 92, 571, 254, 151, 134, 770, 355, 204, 178, 1037
OFFSET
1,6
COMMENTS
Row n partitions A006128 into 4 parts, r(n,0) + r(n,1) + r(n,3) + r(n,4) = p(n) = A006128(n). What is the limiting behavior of r(n,0)/p(n)?
LINKS
EXAMPLE
First 15 rows:
0 1 0 0
0 2 1 0
0 4 1 1
1 7 3 1
1 13 4 2
2 20 9 4
3 32 12 7
7 48 21 10
9 73 29 17
15 106 47 24
21 153 64 37
34 215 97 53
46 303 131 76
68 416 190 106
92 571 254 151
MATHEMATICA
f[n_] := Mod[Flatten[IntegerPartitions[n]], 4];
Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1, 2, 3}] (* A325773 array *)
Flatten[%] (* A325773 sequence *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Jun 05 2019
STATUS
approved