A306403 The number of distinct products that can be formed by multiplying the parts of a partition of n into 3 positive parts.

0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 13, 14, 19, 20, 23, 27, 29, 32, 34, 39, 43, 47, 51, 53, 59, 58, 67, 73, 75, 81, 88, 91, 93, 106, 109, 114, 117, 128, 131, 133, 145, 154, 163, 166, 174, 181, 180, 201, 206, 209, 219, 231, 240, 238, 252, 267, 272, 289, 290, 300, 299, 323, 328, 345, 349, 366, 376

Offset: 0

Author

R. J. Mathar, Feb 13 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• R. J. Mathar, Java program that computes a b-file

Crossrefs

Row sums of A317578.

Cf. A069905.

Programs

Maple

a:= proc(n) option remember; local m, c, i, j, h, w;
      m, c:= proc() true end, 0; forget(m);
      for i to iquo(n, 3) do for j from i to iquo(n-i, 2) do
        h:= i*j*(n-j-i); w:= m(h);
        if w then m(h):= false; c:= c+1 fi
      od od; c
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Feb 13 2019

Mathematica

a[n_] := a[n] = Module[{m, c = 0, i, j, h, w}, m[_] = True; For[i = 1, i <= Quotient[n, 3], i++, For[j = i, j <= Quotient[n - i, 2], j++, h = i*j*(n - j - i); w = m[h]; If[w, m[h] = False; c++]]]; c];
a /@ Range[0, 80] (* Jean-François Alcover, Feb 24 2020, after Alois P. Heinz *)

Formula

a(n) <= A069905(n).