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.

2, 6, 60, 420, 2520, 27720, 360360, 360360, 12252240, 232792560, 232792560, 5354228880, 26771144400, 80313433200, 2329089562800, 72201776446800, 144403552893600, 144403552893600, 5342931457063200

Offset

1,1

Links

Table of n, a(n) for n=1..19.

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

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

Sequence in context: A308532 A102290 A025540 * A226959 A083135 A056604

Adjacent sequences: A334221 A334222 A334223 * A334225 A334226 A334227

Keyword

nonn

Author

Scott R. Shannon and N. J. A. Sloane, May 28 2020

Status

approved