{"id":"e-9dd90579e209f20b","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":"e4371abe6662ec9a1c900759b85cb16f1938b61c752a10a12149d189c1903d0b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":8779,"certificate_compressed_size":2448,"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":[]}