%I #22 Jun 02 2020 08:34:21

%S 2,6,60,420,2520,27720,360360,360360,12252240,232792560,232792560,

%T 5354228880,26771144400,80313433200,2329089562800,72201776446800,

%U 144403552893600,144403552893600,5342931457063200

%N Consider a graph as defined in A306302 formed from a row of n adjacent congruent squares with the diagonals of all possible rectangles; a(n) is the minimum edge length of the squares such that the vertices formed by all intersections have integer x and y coordinates.

%F a(n) = A003418(2n-1) = A076100(n) for n>1.

%e a(1) = 2 as for a single square, with its bottom left corner at the origin, with both diagonals drawn the intersection point of those lines is at (L/2,L/2) where L is the edge length. Thus L=2 for this to have integer coordinates.

%e a(2) = 6 as for two vertically adjacent squares the seven intersection points of the diagonals and shared internal edge have coordinates (L/3,4L/3),(L/2,3L/2),(2L/3,4L/3),(L/2,L),(L/3,2L/3),(L/2,L/2),(2L/3,2L/3). Thus L=6, the lowest common multiple of the denominators, for all these points to have integer coordinates.

%Y Cf. A306302, A003418, A331755, A290132, A290131.

%K nonn

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, May 28 2020