{"schema":"vela.problem-packet.v0.1","problem":669,"statement":"Let $F_k(n)$ be minimal such that for any $n$ points in $\\mathbb{R}^2$ there exist at most $F_k(n)$ many distinct lines passing through at least $k$ of the points, and $f_k(n)$ similarly but with lines passing through exactly $k$ points.Estimate $f_k(n)$ and $F_k(n)$ - in particular, determine $\\lim F_k(n)/n^2$ and $\\lim f_k(n)/n^2$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A003035","name":"Maximal number of 3-tree rows in n-tree orchard problem.","terms":"0,0,1,1,2,4,6,7,10,12,16,19,22,26","url":"https://oeis.org/A003035"},{"id":"A006065","name":"Maximal number of 4-tree rows in n-tree orchard problem.","terms":"0,0,0,1,1,1,2,2,3,5,6,7,9,10,12,15,16,18,20,23","url":"https://oeis.org/A006065"},{"id":"A008997","name":"Orchard problem with 5 trees in a row (may not have all been proved optimal).","terms":"0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,7,9,10,11","url":"https://oeis.org/A008997"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}