{"schema":"vela.problem-packet.v0.1","problem":528,"statement":"Let $f(n,k)$ count the number of self-avoiding walks of $n$ steps (beginning at the origin) in $\\mathbb{Z}^k$ (i.e. those walks which do not intersect themselves). Determine\\[C_k=\\lim_{n\\to\\infty}f(n,k)^{1/n}.\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A156816","name":"Decimal expansion of the positive root of the equation 13x^4 - 7x^2 - 581 = 0.","terms":"2,6,3,8,1,5,8,5,3,0,3,4,1,7,4,0,8,6,8,4,3,0,3,0,7,5,6,6,7,4,4,4,1,3,0,4,8,8,8,0,5,0,2,2,0,1,0,3,1,8,3,5,9,7,3,7,0,7,8,7,","url":"https://oeis.org/A156816"},{"id":"A387897","name":"Decimal expansion of the connective constant of the square lattice.","terms":"2,6,3,8,1,5,8,5,3,0,3,2,7","url":"https://oeis.org/A387897"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}