{"schema":"vela.problem-packet.v0.1","problem":83,"statement":"Suppose that we have a family $\\mathcal{F}$ of subsets of $[4n]$ such that $\\lvert A\\rvert=2n$ for all $A\\in\\mathcal{F}$ and for every $A,B\\in \\mathcal{F}$ we have $\\lvert A\\cap B\\rvert \\geq 2$. Then\\[\\lvert \\mathcal{F}\\rvert \\leq \\frac{1}{2}\\left(\\binom{4n}{2n}-\\binom{2n}{n}^2\\right).\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A071799","name":"Number of lattice paths in the lattice [0..2n] X [0..2n] which do not pass through the point (n,n).","terms":"2,34,524,7970,121252,1850380,28337976,435443490,6711230900,103711749284,1606464657096,24935144010764,387746052588104,603","url":"https://oeis.org/A071799"},{"id":"A387635","name":"a(n) = Sum_{k=0..n-1} binomial(2*n, k)^2.","terms":"0,1,17,262,3985,60626,925190,14168988,217721745,3355615450,51855874642,803232328548,12467572005382,193873026294052,30196","url":"https://oeis.org/A387635"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}