A306435 Number of distinct integers that are product of the parts of exactly one partition of n into 3 positive parts.

0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 12, 12, 19, 19, 22, 27, 28, 31, 31, 38, 42, 46, 50, 50, 57, 51, 64, 71, 70, 77, 85, 86, 84, 104, 104, 108, 108, 123, 122, 119, 136, 147, 158, 156, 164, 170, 162, 194, 195, 193, 205, 219, 228, 215, 233, 254, 254, 278

Offset: 0

Author

Alois P. Heinz, Feb 15 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=1 of A317578.

Programs

Maple

a:= proc(n) option remember; local m, c, i, j, h, w;
      m, c:= proc() 0 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=0 then m(h):= 1; c:= c+1
      elif w=1 then m(h):= 2; c:= c-1
        fi
      od od; c
    end:
seq(a(n), n=0..80);

Mathematica

a[n_] := a[n] = Module[{m, c = 0, i, j, h, w}, m[_] = 0; 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==0, m[h] = 1; c++; If[w==1, m[h] = 2; c--]]]]; c];
a /@ Range[0, 80] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)