{"id":"e-0292c31bd110411a","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-7b3743413970d91c","premise_count":0,"theorem":"L. L. Liu and Y. Wang, Adv. Appl. Math. 38 (2007) 542-560, Theorem 2.1 and Corollary 2.4 (A unified approach to polynomial sequences with only real zeros; the lag row as the interlacer, b_n = 0), weak interlacing of consecutive rows, with nonnegativity of the coefficients replaced, where a root region is certified, by an exact root-location induction","lean_route":null,"lean_declarations":["RealRooted.MaWang.strictInterl_of_interlaces_evalCoeff_nonpos"],"certificate_hash":"68087fb75a53c74d318a7099cdd72e829337b4f5a7c0cab2dbe7bcaa9d06da9b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":4457,"certificate_compressed_size":1406,"conclusion_name":"theta_plus_one of a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-7b3743413970d91c","claim":"one_signed_coefficients"},{"node_id":"n-7b3743413970d91c","claim":"hadamard_kernel"},{"node_id":"n-7b3743413970d91c","claim":"real_rooted"}]}