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%I #16 Oct 27 2023 21:13:58
%S 1,1,1,2,3,5,7,10,13,18,22,28,33,40,46,56,64,75,84,97,109,125,137,156,
%T 170,192,210,232,251,276,296,322,347,376,400,435,463,498,529,567,600,
%U 641,674,720,758,808,849,901,942,1001,1051,1110,1157,1225,1275
%N Number of distinct products i*j*k over all triples (i,j,k) with i,j,k>=0 and i+j+k <= n.
%C This sequence is in reply to an extension request made in A100450.
%H Alois P. Heinz, <a href="/A213213/b213213.txt">Table of n, a(n) for n = 0..1000</a> (terms n = 0..200 from Robert Price)
%F a(n) = (A213207(n)+1)/2.
%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) +b(n)) end:
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Mar 02 2013
%t f[n_] := Length[ Union[ Flatten[ Table[ If[ i+j+k <= n, i*j*k, 0], {i, 0, n}, {j, 0, n}, {k, 0, n}], 2]]]; Table[ f[n], {n, 0, 200}]
%Y Cf. A018805, A027430, A100448, A100449, A100450, A213207, A213208, A213212.
%K nonn,easy
%O 0,4
%A _Robert Price_, Mar 02 2013
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