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%I #9 Oct 22 2018 17:40:47
%S 1,2,4,8,12,18,27,36,48,64,80,100,125,150,180,216,252,294,343,392,448,
%T 512,576,648,729,810,900,1000,1100,1210,1331,1452,1584,1728,1872,2028,
%U 2197,2366
%N Maximal product of three numbers with sum n: a(n) = max(r*s*t), n = r+s+t.
%C Identical to A006501.
%F Same iteration as in A002620 (in two dimensions) but here in three dimensions: Index 0 (mod 3) terms are cubes and sequence pass from one cube to the next one extending successively each side by one unity: n^3, n^2(n+1), n(n+1)^2, (n+1)^3. - _Alexandre Wajnberg_, Dec 29 2005
%F From _Chai Wah Wu_, Oct 22 2018: (Start)
%F a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) - a(n-8) for n > 10.
%F G.f.: x^3*(x^2 + 1)/((x - 1)^4*(x^2 + x + 1)^2). (End)
%e a(13) = 80 = 4*4*5, another partition is 5,5,3 giving the product 75.
%Y Cf. A002620.
%K nonn
%O 3,2
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003
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