{"paper":{"title":"Explicit formula for the generating series of diagonal 3D rook paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.SC","authors_text":"Alin Bostan, Fr\\'ed\\'eric Chyzak, Lucien Pech, Mark van Hoeij","submitted_at":"2011-05-23T10:12:12Z","abstract_excerpt":"Let $a_n$ denote the number of ways in which a chess rook can move from a corner cell to the opposite corner cell of an $n \\times n \\times n$ three-dimensional chessboard, assuming that the piece moves closer to the goal cell at each step. We describe the computer-driven \\emph{discovery and proof} of the fact that the generating series $G(x)= \\sum_{n \\geq 0} a_n x^n$ admits the following explicit expression in terms of a Gaussian hypergeometric function: \\[ G(x) = 1 + 6 \\cdot \\int_0^x \\frac{\\,\\pFq21{1/3}{2/3}{2} {\\frac{27 w(2-3w)}{(1-4w)^3}}}{(1-4w)(1-64w)} \\, dw.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4456","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}