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

0,6

Links

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

R. J. Mathar, Java program that computes a b-file

Formula

a(n) <= A069905(n).

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 *)

Crossrefs

Row sums of A317578.

Cf. A069905.

Sequence in context: A317578 A306435 A034155 * A129590 A261132 A262525

Adjacent sequences: A306400 A306401 A306402 * A306404 A306405 A306406

Keyword

nonn

Author

R. J. Mathar, Feb 13 2019

Status

approved