A266480 Maximal product of multiplicities of parts of a partition of n.

1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, 50, 56, 64, 72, 84, 96, 108, 120, 135, 150, 165, 180, 200, 220, 240, 264, 288, 312, 336, 364, 405, 450, 495, 540, 600, 660, 720, 792, 864, 936, 1008, 1092, 1176, 1260, 1365, 1470, 1575

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..16000 (terms 0..5000 from Alois P. Heinz)

Example

a(4) = 4 because the products of the multiplicities of the parts in the partitions [4], [1,3], [2,2], [1,1,2], [1,1,1,1] are 1, 1, 2, 2, 4, respectively.
a(21) = 7*4*2 = 56 for partition [1,1,1,1,1,1,1,2,2,2,2,3,3].

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, max(1, n),
      max(seq(b(n-i*j, i-1)*max(1, j), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..100);

Mathematica

Table[Max@ Map[Times @@ Map[Last, Tally@ #] &, IntegerPartitions@ n], {n, 0, 56}] (* Michael De Vlieger, Dec 31 2015 *)
b[n_, i_] := b[n, i] = If[n==0 || i==1, Max[1, n], Max[Table[b[n-i*j, i-1]*Max[1, j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 01 2016, after Alois P. Heinz *)

Crossrefs

Row lengths of A266477.

Cf. A266871.

Sequence in context: A003045 A279079 A029750 * A246080 A278619 A173925

Adjacent sequences: A266477 A266478 A266479 * A266481 A266482 A266483

Keyword

nonn

Author

Emeric Deutsch and Alois P. Heinz, Dec 29 2015

Status

approved