A306435 - OEIS

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

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OFFSET

0,6

LINKS

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

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

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 *)

CROSSREFS

Column k=1 of A317578.

Sequence in context: A317296 A103740 A317578 * A034155 A306403 A129590

Adjacent sequences: A306432 A306433 A306434 * A306436 A306437 A306438

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 15 2019

STATUS

approved