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A306403 The number of distinct products that can be formed by multiplying the parts of a partition of n into 3 positive parts. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 23:38 EST 2021. Contains 349558 sequences. (Running on oeis4.)