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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,4 COMMENTS The car starts and finishes on the positive x-axis, 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 Table of n, a(n) for n=6..25. Pontus von Brömssen, Some optimal Racetrack trajectories for A351349/A351350. Wikipedia, Racetrack FORMULA a(n)/A351350(n) >= A351351(n)/A351352(n). 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 . . n = 7 (r^2 = 1 = a(7)/A351350(7)): . 2 . 1 . 3 . * . 7 . 5 . 6 . . n = 9 (r^2 = 4 = a(9)/A351350(9)): . 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 Cf. A351041, A351350 (denominators), A351351, A351352. Sequence in context: A107053 A327303 A337302 * A222271 A068376 A131592 Adjacent sequences: A351346 A351347 A351348 * A351350 A351351 A351352 KEYWORD nonn,frac,more AUTHOR Pontus von Brömssen, Feb 09 2022 STATUS approved

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Last modified November 28 02:41 EST 2023. Contains 367394 sequences. (Running on oeis4.)