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A325774
Rectangular array: row n shows the number of parts in all partitions of n that are == k (mod 5), for k = 0, 1, 2, 3, 4.
4
0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 4, 1, 1, 0, 0, 7, 3, 1, 1, 1, 12, 4, 2, 1, 1, 20, 8, 4, 2, 2, 31, 12, 6, 3, 3, 47, 20, 10, 6, 5, 70, 28, 16, 9, 9, 102, 44, 23, 14, 13, 147, 61, 34, 20, 19, 208, 91, 50, 31, 28, 290, 124, 71, 43, 40, 400, 178, 99, 63, 58, 546
OFFSET
1,7
COMMENTS
Row n partitions A006128 into 5 parts, r(n,0) + r(n,1) + r(n,3) + r(n,4) + r(n,5) = 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
0 2 1 0 0
0 4 1 1 0
0 7 3 1 1
1 12 4 2 1
1 20 8 4 2
2 31 12 6 3
3 47 20 10 6
5 70 28 16 9
9 102 44 23 14
13 147 61 34 20
19 208 91 50 31
28 290 124 71 43
40 400 178 99 63
58 546 239 139 86
MATHEMATICA
f[n_] := Mod[Flatten[IntegerPartitions[n]], 5];
Table[Count[f[n], k], {n, 1, 40}, {k, 0, 1, 2, 3, 4}] (* A325774 array *)
Flatten[%] (* A325773 sequence *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Jun 05 2019
STATUS
approved