A290190 Minimum sum of mutual Manhattan distances of n distinct grid points in a cubic lattice.

1, 4, 8, 16, 25, 36, 48, 68, 89, 112, 136, 168

Offset

2,2

Comments

Sum of mutual L1-distances of locations in a 3-dimensional n-town of optimum shape.

Links

Table of n, a(n) for n=2..13.

Example

a(2)=1: Grid points (1 2 2),(1 1 2)
a(3)=4: (1 1 1),(1 2 1),(2 1 1)
a(4)=8: (1 1 1),(2 1 1),(1 2 1),(2 2 1)
a(5)=16: (1 2 2),(2 2 1),(2 2 2),(1 1 1),(1 2 1)
a(6)=25: (2 1 2),(1 1 1),(2 2 1),(2 1 1),(1 2 1),(2 2 2)
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)

Crossrefs

Cf. A193452.

Sequence in context: A161226 A369566 A022560 * A193452 A003451 A277029

Adjacent sequences: A290187 A290188 A290189 * A290191 A290192 A290193

Keyword

nonn,more

Author

Hugo Pfoertner, Jul 23 2017

Status

approved