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%I #7 Jul 24 2017 01:59:39
%S 1,4,8,16,25,36,48,68,89,112,136,168
%N Minimum sum of mutual Manhattan distances of n distinct grid points in a cubic lattice.
%C Sum of mutual L1-distances of locations in a 3-dimensional n-town of optimum shape.
%e a(2)=1: Grid points (1 2 2),(1 1 2)
%e a(3)=4: (1 1 1),(1 2 1),(2 1 1)
%e a(4)=8: (1 1 1),(2 1 1),(1 2 1),(2 2 1)
%e a(5)=16: (1 2 2),(2 2 1),(2 2 2),(1 1 1),(1 2 1)
%e a(6)=25: (2 1 2),(1 1 1),(2 2 1),(2 1 1),(1 2 1),(2 2 2)
%e a(10)=89: (2 2 2),(1 3 1),(1 1 1),(1 2 2),(2 3 2),(2 1 1),(1 3 2),(1 2 1),(2 2 1),(2 3 1)
%Y Cf. A193452.
%K nonn,more
%O 2,2
%A _Hugo Pfoertner_, Jul 23 2017
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