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A102534 Number of distinct values of i*j + j*k + k*i with 1 <= i<= j < k <= n.

%I A102534 #9 Dec 16 2024 02:09:05
%S A102534 0,1,4,10,19,33,49,70,96,127,161,201,238,287,337,390,449,519,586,662,
%T A102534 741,818,902,997,1095,1194,1299,1410,1518,1651,1778,1908,2054,2186,
%U A102534 2332,2493,2636,2793,2955,3128,3300,3481,3660,3840,4050,4252,4443,4665,4871
%N A102534 Number of distinct values of i*j + j*k + k*i with 1 <= i<= j < k <= n.
%H A102534 Robert Israel, <a href="/A102534/b102534.txt">Table of n, a(n) for n = 1..2000</a>
%p A102534 F:= proc(n) local i,j;
%p A102534       {seq(seq(i*j + (i+j)*n, i=1..j),j=1..n-1)}
%p A102534 end proc:
%p A102534 R:= NULL:
%p A102534 S:= {}:
%p A102534 for n from 1 to 100 do
%p A102534   S:= S union F(n);
%p A102534   R:= R,nops(S);
%p A102534 od:
%p A102534 R; # _Robert Israel_, Dec 15 2024
%t A102534 f[n_] := Length[ Union[ Flatten[ Table[i*j + j*k + k*i, {i, n}, {j, i, n}, {k, j + 1, n}]]]]; Table[ f[n], {n, 48}] (* _Robert G. Wilson v_, Jan 13 2005 *)
%Y A102534 Cf. A100439, A100440, A102533.
%K A102534 nonn
%O A102534 1,3
%A A102534 _Robert G. Wilson v_, Jan 13 2005