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Number of distinct products i*j*k over all triples (i,j,k) with |i| + |j| + |k| <= n.
10

%I #25 Oct 27 2023 21:15:07

%S 1,1,1,3,5,9,13,19,25,35,43,55,65,79,91,111,127,149,167,193,217,249,

%T 273,311,339,383,419,463,501,551,591,643,693,751,799,869,925,995,1057,

%U 1133,1199,1281,1347,1439,1515,1615,1697,1801,1883,2001,2101,2219,2313

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

%C This sequence is in reply to an extension request made in A100450.

%H 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 h:= proc() true end:

%p b:= proc(n) local c, i, j, p;

%p c:=0;

%p for i to iquo(n, 3) do

%p for j from i to iquo(n-i, 2) do p:= i*j*(n-i-j);

%p if h(p) then h(p):= false; c:=c+1 fi

%p od

%p od; c

%p end:

%p a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +2*b(n)) end:

%p seq(a(n), n=0..60); # _Alois P. Heinz_, Mar 02 2013

%t 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 Cf. A018805, A027430, A100448, A100449, A100450, A213208, A213212, A213213.

%K nonn,easy

%O 0,4

%A _Robert Price_, Mar 01 2013