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A334224
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.
0
2, 6, 60, 420, 2520, 27720, 360360, 360360, 12252240, 232792560, 232792560, 5354228880, 26771144400, 80313433200, 2329089562800, 72201776446800, 144403552893600, 144403552893600, 5342931457063200
OFFSET
1,1
FORMULA
a(n) = A003418(2n-1) = A076100(n) for n>1.
EXAMPLE
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.
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved