{"id":"W2401300893","doi":"","title":"On two types of (2, k)-distance Lucas numbers.","year":2014,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Lucas number; Lucas sequence; Combinatorics; Fibonacci number; Fibonacci polynomials; Difference polynomials","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00006103787,0.00007136714,0.000129567,0.000009196691,0.00005056952,0.000007039287,0.0001057268,0.0000112294,0.0002148996],"category_scores_gemma":[0.00001454213,0.00006296591,0.00004329206,0.00008424575,0.00005034784,0.00003034516,0.00002134912,0.00005977993,0.00009375641],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006013518,"about_ca_system_score_gemma":0.000006215273,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009875541,"about_ca_topic_score_gemma":2.118515e-7,"domain_scores_codex":[0.9995759,0.0000133846,0.0001220838,0.000107961,0.00007492265,0.0001057084],"domain_scores_gemma":[0.9994333,0.0001787099,0.00006902761,0.000244813,0.00003495732,0.00003921662],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000004371474,0.0001004072,0.0002254583,0.000005469631,0.000009632265,2.898503e-8,0.00003239009,0.00002917172,0.00007642666,0.9968081,0.0003536695,0.002354872],"study_design_scores_gemma":[0.0003068314,0.00002794866,0.00003367121,0.00001478519,0.000006885462,4.859182e-8,0.00003001869,0.0001849991,0.002470214,0.9885514,0.008304801,0.00006840433],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.4383648,0.0000181028,0.08775996,0.0002050854,0.0004462131,0.0002276414,0.00002250162,0.00005452059,0.4729012],"genre_scores_gemma":[0.9984873,3.508707e-7,0.0009511605,0.00002562708,0.00001398279,0.00001749914,0.000005151433,0.000009484644,0.0004894383],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5601225,"threshold_uncertainty_score":0.2567675,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005955624869890068,"score_gpt":0.263778302223478,"score_spread":0.2578226773535879,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}