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A213207 Number of distinct products i*j*k over all triples (i,j,k) with |i| + |j| + |k| <= n.

%I A213207 #25 Oct 27 2023 21:15:07
%S A213207 1,1,1,3,5,9,13,19,25,35,43,55,65,79,91,111,127,149,167,193,217,249,
%T A213207 273,311,339,383,419,463,501,551,591,643,693,751,799,869,925,995,1057,
%U A213207 1133,1199,1281,1347,1439,1515,1615,1697,1801,1883,2001,2101,2219,2313
%N A213207 Number of distinct products i*j*k over all triples (i,j,k) with |i| + |j| + |k| <= n.
%C A213207 This sequence is in reply to an extension request made in A100450.
%H A213207 Alois P. Heinz, <a href="/A213207/b213207.txt">Table of n, a(n) for n = 0..1000</a> (terms n = 0..100 from Robert Price)
%p A213207 h:= proc() true end:
%p A213207 b:= proc(n) local c, i, j, p;
%p A213207       c:=0;
%p A213207       for i to iquo(n, 3) do
%p A213207         for j from i to iquo(n-i, 2) do p:= i*j*(n-i-j);
%p A213207           if h(p) then h(p):= false; c:=c+1 fi
%p A213207         od
%p A213207       od; c
%p A213207     end:
%p A213207 a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +2*b(n)) end:
%p A213207 seq(a(n), n=0..60);  # _Alois P. Heinz_, Mar 02 2013
%t A213207 f[n_] := Length[ Union[ Flatten[ Table[ If[ Abs[i] + Abs[j] + Abs[k] <= n, {i*j*k}, {0}], {i, -n, n}, {j, -n, n}, {k, -n, n}], 2]]]; Table[ f[n], {n, 0, 100}]
%Y A213207 Cf. A018805, A027430, A100448, A100449, A100450, A213208, A213212, A213213.
%K A213207 nonn,easy
%O A213207 0,4
%A A213207 _Robert Price_, Mar 01 2013