{"id":"W2406434350","doi":"","title":"Distance Fibonacci numbers, distance Lucas numbers and their applications.","year":2013,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Fibonacci number; Mathematics; Lucas number; Lucas sequence; Pisano period; Arithmetic; Combinatorics; Discrete mathematics; Fibonacci 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000740058,0.0008603754,0.0008177617,0.004348679,0.001808067,0.003161086,0.0008346293,0.001769269,0.009618923],"category_scores_gemma":[0.004308526,0.0004932616,0.0005374403,0.004396116,0.003273166,0.004932705,0.001946001,0.00278596,0.002175275],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001520515,"about_ca_system_score_gemma":0.0005380423,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001165294,"about_ca_topic_score_gemma":0.001641009,"domain_scores_codex":[0.999543,0.0001335669,0.00003389224,0.00006965925,0.0001731387,0.00004684164],"domain_scores_gemma":[0.9988629,0.0006964838,0.0001278189,0.00006768428,0.0001572341,0.00008804396],"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":[0.000008545027,0.00000741314,0.00009393819,0.00006726854,0.000004426179,0.00005366145,0.00009793696,0.0004055657,0.0001625675,0.9836212,0.004387149,0.01109028],"study_design_scores_gemma":[0.000002938277,0.000007640538,0.0001370365,0.00003556755,0.000004050949,0.0001657167,0.00009124904,0.001103093,0.00007370928,0.9733413,0.02502924,0.000008410333],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.04802461,0.2989922,0.1356389,0.01046446,0.006207427,0.00005578732,0.0005073543,0.0003147993,0.4997946],"genre_scores_gemma":[0.6615114,0.1141102,0.09448286,0.003944032,0.009155377,0.0002236242,0.0006480934,0.000177956,0.1157465],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009618923,"threshold_uncertainty_score":0.03217846,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.004838139742126608,"score_gpt":0.2312477579736204,"score_spread":0.2264096182314938,"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."}}