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"Connect the dots": Minimal number of circular arcs needed to connect all points of an n X n grid of points.
1

%I #13 Mar 15 2021 21:30:58

%S 1,1,3,3,5,6,9

%N "Connect the dots": Minimal number of circular arcs needed to connect all points of an n X n grid of points.

%C a(7)=9 is only a conjecture at present. I include it in the Data line to disambiguate this sequence from its neighbors.

%C For straight line segments the answer is conjectured to be 2n-2 for all n >=3, with a(1)=1, a(2)=3.

%H S. W. Golomb and John Selfridge, <a href="http://www.ams.org/mathscinet-getitem?mr=268063">Unicursal Polygonal Paths and Other Graphs on Point Lattices</a>, Pi Mu Epsilon Journal 5 (1970) 107-117.

%H Ed Pegg, Jr., <a href="http://www.mathpuzzle.com/dots.html">Connect the dots - Arcs</a>

%K nonn,more

%O 1,3

%A _N. J. A. Sloane_, Mar 12 2011