A350155: a(n) is the greatest number of times that a laser can hit a reflector on an n X n grid. Reflectors are shown as '\' or '/', empty locations are '.', and the starting location of the laser is 'V'. Found by Dmitry Kamenetsky and Benjamin Butin, 28th January 2022. The following are new patterns that improve previous results. In particular the number of hits in an n X n pattern p(n) grows exponentially: p(n+2) = 4 * p(n) + 6n + 14. For odd n: a(n) >= p(n) = 7 * 2^(n-1) - 2n - 6. For example, for n = 7 we get 428 hits with the following pattern: V \\...\\ .\\.\\. ..\\\.. ../.\.. ..\\/.. .\\.//. \\...// For even n: a(n) >= p(n) = 13 * 2^(n-2) - 2n - 6. For example, for n = 8 we get 810 hits with the following pattern: V \\....\\ .\\..\\. ..\\\\.. ...\\... ../..\.. ..\\//.. .\\..//. \\....//