A364810 a(n) = greatest number in row n of the array in A225485.

1, 1, 1, 2, 3, 4, 8, 9, 12, 17, 26, 27, 44, 53, 76, 98, 128, 168, 212, 273, 344, 429, 525, 662, 796, 981, 1182, 1442, 1709, 2096, 2663, 3406, 4315, 5426, 6784, 8417, 10466, 12824, 15721, 19104, 23267, 27981, 33856, 40515, 48508, 57826, 68982, 81493, 96869

Offset

1,4

Comments

a(n) = the greatest number of partitions of n that all have the same frequency depth (as in A225485); this is also the greatest number of partitions of n that all have the same adjusted frequency depth (A325245).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Example

Following the example in A225485, the frequency depths for the partitions of 8 are 1,2,3,4,5, and these occur 1,3,6,9,3 times, respectively. The greatest of these is 9, so that a(8) = 9.

Mathematica

c[s_] := c[s] = Select[Table[Count[s, i], {i, 1, Max[s]}], # > 0 &];
f[s_] := f[s] = Drop[FixedPointList[c, s], -2];
t[s_] := t[s] = Length[f[s]];
u[n_] := u[n] = Table[t[Part[IntegerPartitions[n], i]], {i, 1, Length[IntegerPartitions[n]]}];
v = Table[Count[u[n], k], {n, 2, 12}, {k, 1, Max[u[n]]}]
Map[Max, v]

Crossrefs

Cf. A000041, A225485, A225486, A325245.

Sequence in context: A018231 A332622 A085256 * A335761 A127483 A130804

Adjacent sequences: A364807 A364808 A364809 * A364811 A364812 A364813

Keyword

nonn

Author

Clark Kimberling, Sep 14 2023

Extensions

a(36)-a(49) from Alois P. Heinz, Sep 15 2023

Status

approved