A049031 - OEIS

A049031

Maximization of sums of cubes of integer differences (b_[ i ]-i)^3 over permutations {b_[ i ], for i-1,2,...,n} on first n integers.

%I #10 Sep 30 2016 06:50:19

%S 0,0,2,8,20,40,80,140,224,336,504,720,990,1320,1760,2288,2912,3640,

%T 4550,5600,6800,8160,9792,11628,13680,15960,18620,21560,24794,28336,

%U 32384,36800,41600,46800,52650,58968,65772,73080,81200,89900

%N Maximization of sums of cubes of integer differences (b_[ i ]-i)^3 over permutations {b_[ i ], for i-1,2,...,n} on first n integers.

%H D. C. Blest, <a href="http://www.jstor.org/stable/3620788">Optimising Sums of Cubes of Integer Differences</a>, Math. Gaz., Vol. 84, No. 501 (Nov., 2000), pp. 509-513.

%F a[ n ] = (Sum_{i=1}^{i=r} [ (n+1-2i)^3-(n-r)*r^3 ]) / 3 where r=floor((n+2)/4)).

%F a(n) = r*(n-r+1)*(n-r)*(n-r-1)/3, where r = floor((n+1)/4). - _Vladeta Jovovic_, Dec 22 2004

%F G.f.: 2*x^3*(1+2*x+3*x^2+4*x^3+7*x^4+4*x^5+3*x^6+2*x^7+x^8)/((1+x)^3*(1+x^2)^3*(1-x)^5). - _Vladeta Jovovic_, Dec 22 2004

%t a[n_] := With[{r = Floor[(n+1)/4]}, r*(n-r+1)*(n-r)*(n-r-1)/3]; Array[a, 40] (* _Jean-François Alcover_, Sep 30 2016, after _Vladeta Jovovic_ *)

%Y Cf. A049032.

%K nonn,nice,easy

%O 1,3

%A David C Blest (D.Blest(AT)utas.edu.au)