{"id":"e-46106635735db081","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-e3d901814302c059","premise_count":0,"theorem":"all-index identity Q_n = P_n certified by exact Ore-algebra division and identifying rows (polytool preserver-image certificate of the identity map)","lean_route":null,"lean_declarations":[],"certificate_hash":"563bffa72448f0a4a7237e566fd717abde4277d218fdfe49944a95ab86692263","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":6710,"certificate_compressed_size":2038,"conclusion_name":"Triangle read by rows: T(n,k) is the number of ways to tile a 3 X n rectangle with k pieces of 2 X 2 tiles and 3n-4k pieces of 1 X 1 tiles (0 <= k <= floor(n/2)).","claims":[],"premises":[],"cited_by":[]}