{"id":"W2756505774","doi":"","title":"On Bi-Periodic Fibonacci And Lucas Numbers by Matrix Method.","year":2017,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Fibonacci number; Lucas number; Mathematics; Lucas sequence; Pisano period; Fibonacci polynomials; Combinatorics; Arithmetic","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":[0.0005672611,0.0008601639,0.000750736,0.003012876,0.001210143,0.001813127,0.001094899,0.001049044,0.01342642],"category_scores_gemma":[0.002652899,0.0003872727,0.0007682787,0.001365012,0.001689925,0.00288306,0.001526122,0.001699948,0.003505154],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008654188,"about_ca_system_score_gemma":0.000681561,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001439332,"about_ca_topic_score_gemma":0.003212505,"domain_scores_codex":[0.9996815,0.0001108955,0.00001267461,0.00003718029,0.0001182845,0.00003949216],"domain_scores_gemma":[0.999532,0.0001857434,0.00004878395,0.00005696687,0.0001196987,0.00005679085],"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":[0.00001346736,0.00001266074,0.00006704378,0.00005344024,0.000006561289,0.00005626973,0.0001080105,0.002004575,0.0006750128,0.9842918,0.003408596,0.009302481],"study_design_scores_gemma":[0.00001336516,0.00001502161,0.0001163232,0.00004027812,0.000007020119,0.0001320393,0.00006047073,0.03205569,0.0003608257,0.9568013,0.01038042,0.00001717005],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07460614,0.007558085,0.7158794,0.002097824,0.002267713,0.0001543684,0.0004751531,0.0005418742,0.1964193],"genre_scores_gemma":[0.5487174,0.005246453,0.3391896,0.0009364739,0.001670976,0.0004280122,0.0006091663,0.0007067537,0.1024952],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01342642,"threshold_uncertainty_score":0.04491585,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008926138536508246,"score_gpt":0.3210268394270249,"score_spread":0.3121007008905167,"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."}}