A102533 Number of distinct values of i*j + j*k + k*i with 1 <= i < j <= k <= n.

0, 1, 4, 10, 20, 35, 50, 72, 100, 129, 163, 203, 244, 290, 346, 400, 461, 526, 600, 676, 756, 836, 925, 1018, 1117, 1220, 1325, 1435, 1554, 1683, 1811, 1938, 2078, 2212, 2367, 2526, 2677, 2835, 3003, 3169, 3350, 3527, 3714, 3898, 4099, 4304, 4498, 4713

Offset: 1

Author

Robert G. Wilson v, Jan 13 2005

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A100439, A100440, A102534.

Programs

Maple

F:= proc(n) local i,j;
      {seq(seq(i*j + (i+j)*n, i=1..j-1),j=2..n)}
end proc:
R:= NULL:
S:= {}:
for n from 1 to 50 do
  S:= S union F(n);
  R:= R, nops(S);
od:
R; # Robert Israel, Dec 15 2024

Mathematica

f[n_] := Length[ Union[ Flatten[ Table[i*j + j*k + k*i, {i, n}, {j, i + 1, n}, {k, j, n}] ]]]; Table[ f[n], {n, 48}]

Extensions

Offset corrected by Robert Israel, Dec 15 2024