{"id":"e-46ee23218258c2c9","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-e189038e95d51606","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":"859516f42b4a18617f2b11e387a7357c1b38be1cd5da664b956cf38a307b0269","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":6710,"certificate_compressed_size":2040,"conclusion_name":"Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by rows.","claims":[],"premises":[],"cited_by":[]}