

A085891


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


0



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
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OFFSET

3,2


COMMENTS

Identical to A006501.


LINKS

Table of n, a(n) for n=3..40.


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(n1)  a(n2) + 2*a(n3)  4*a(n4) + 2*a(n5)  a(n6) + 2*a(n7)  a(n8) for n > 10.
G.f.: x^3*(x^2 + 1)/((x  1)^4*(x^2 + x + 1)^2). (End)


EXAMPLE

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


CROSSREFS

Cf. A002620.
Sequence in context: A343949 A284122 A212585 * A006501 A224814 A224810
Adjacent sequences: A085888 A085889 A085890 * A085892 A085893 A085894


KEYWORD

nonn


AUTHOR

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


STATUS

approved



