

A123689


Number of points in a square lattice covered by a circle of diameter n if the center of the circle is chosen such that the circle covers the minimum possible number of lattice points.


5



0, 2, 4, 10, 16, 26, 32, 46, 60, 74, 88, 108, 124, 146, 172, 194, 216, 248, 276, 308
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OFFSET

1,2


COMMENTS

a(n)<=min(A053411(n),A053414(n),A053415(n)).


LINKS

Table of n, a(n) for n=1..20.
Hugo Pfoertner, Minimal number of points in the square lattice covered by circular disks. Illustrations.


EXAMPLE

a(1)=0: Circle with diameter 1 with center (0.5,0.5) covers no lattice points; a(2)=2: Circle with diameter 2 with center (0,eps) covers 2 lattice points;
a(3)=4: Circle with diameter 3 with center (0.5,0.5) covers 4 lattice points.


CROSSREFS

Cf. A123690, A053411, A053414, A053415, A122224.
The corresponding sequences for the hexagonal lattice and the honeycomb net are A125851 and A127405, respectively.
Sequence in context: A218665 A189558 A111149 * A137928 A144834 A006584
Adjacent sequences: A123686 A123687 A123688 * A123690 A123691 A123692


KEYWORD

more,nonn


AUTHOR

Hugo Pfoertner, Oct 09 2006


STATUS

approved



