A085891 Maximal product of three numbers with sum n: a(n) = max(r*s*t), n = r+s+t.

1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 80, 100, 125, 150, 180, 216, 252, 294, 343, 392, 448, 512, 576, 648, 729, 810, 900, 1000, 1100, 1210, 1331, 1452, 1584, 1728, 1872, 2028, 2197, 2366

Offset: 3

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003

Keywords

• nonn
• easy

Comments

Apart from offset identical to A006501.

Examples

			a(13) = 80 = 4*4*5, another partition is 5,5,3 giving the product 75.
		

Crossrefs

Cf. A002620.

Formula

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

From Chai Wah Wu, Oct 22 2018: (Start)

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.

G.f.: x^3*(x^2 + 1)/((x - 1)^4*(x^2 + x + 1)^2). (End)