cp's OEIS Frontend

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

%I A102533 #8 Dec 16 2024 02:08:47
%S A102533 0,1,4,10,20,35,50,72,100,129,163,203,244,290,346,400,461,526,600,676,
%T A102533 756,836,925,1018,1117,1220,1325,1435,1554,1683,1811,1938,2078,2212,
%U A102533 2367,2526,2677,2835,3003,3169,3350,3527,3714,3898,4099,4304,4498,4713
%N A102533 Number of distinct values of i*j + j*k + k*i with 1 <= i < j <= k <= n.
%H A102533 Robert Israel, <a href="/A102533/b102533.txt">Table of n, a(n) for n = 1..2000</a>
%p A102533 F:= proc(n) local i,j;
%p A102533       {seq(seq(i*j + (i+j)*n, i=1..j-1),j=2..n)}
%p A102533 end proc:
%p A102533 R:= NULL:
%p A102533 S:= {}:
%p A102533 for n from 1 to 50 do
%p A102533   S:= S union F(n);
%p A102533   R:= R, nops(S);
%p A102533 od:
%p A102533 R; # _Robert Israel_, Dec 15 2024
%t A102533 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}]
%Y A102533 Cf. A100439, A100440, A102534.
%K A102533 nonn
%O A102533 1,3
%A A102533 _Robert G. Wilson v_, Jan 13 2005
%E A102533 Offset corrected by _Robert Israel_, Dec 15 2024