

A351349


Numerator of the square of the radius of the largest circle, centered at the origin, around which a Racetrack car (using Moore neighborhood) can run a full lap in n steps.


4



1, 1, 1, 4, 4, 81, 9, 16, 16, 576, 36, 36, 64, 81, 1250, 100, 144, 144, 8100, 225
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OFFSET

6,4


COMMENTS

The car starts and finishes on the positive xaxis, as in A351041.
The square of the radius of the largest circle is a rational number, because the squared distance from the origin to a line segment between two points with integer coordinates is always rational.


LINKS



FORMULA



EXAMPLE

The following diagrams show examples of optimal trajectories for some values of n. The position of the car after k steps is labeled with the number k. If a number is missing, it means that the car stands still on that step. If the number 0 is missing (for the starting position), it means that the starting and finishing positions coincide. The origin is marked with an asterisk.
.
n = 6 (r^2 = 1/2 = a(6)/A351350(6)):
. 1 .
3 * 6
4 5 .
.
. 2 . 1 .
3 . * . 7
. 5 . 6 .
.
. 3 . 2 .
4 . . . 1
. . * . 9
5 . . . 8
. 6 . 7 .
.
n = 11 (r^2 = 81/10 = a(11)/A351350(11)):
. 4 . 3 . . . . . .
5 . . . . . 2 . . .
. . . . . . . . 1 .
6 . . * . . . . 11 0
. . . . . . . . . .
7 . . . . . 10 . . .
. 8 . 9 . . . . . .
.
n = 12 (r^2 = 9 = a(12)/A351350(12)):
. . . 4 . 3 . . .
. 5 . . . . . 2 .
. . . . . . . . 1
6 . . . * . . . 12
7 . . . . . . . .
. 8 . . . . . 11 .
. . . 9 . 10 . . .


CROSSREFS



KEYWORD

nonn,frac,more


AUTHOR



STATUS

approved



