{"id":"W97847320","doi":"","title":"The Lucas Matrix of Order 2k Sequence {L(2k)n).","year":2001,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Sequence (biology); Order (exchange); Lucas sequence; Combinatorics; Biology; Genetics; Economics","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":[0.0001039484,0.00008719772,0.0001210513,0.000008643165,0.0001915956,0.00002150871,0.0002170865,0.0000182379,0.0001763511],"category_scores_gemma":[0.00001817244,0.00006108295,0.00005162759,0.0002301512,0.0001226647,0.00005891097,0.00005624226,0.00008772704,0.00006739319],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009719648,"about_ca_system_score_gemma":0.0000254832,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001987763,"about_ca_topic_score_gemma":3.829853e-7,"domain_scores_codex":[0.999395,0.00001669439,0.0001902069,0.0001140116,0.0001056677,0.0001784854],"domain_scores_gemma":[0.9992018,0.0002220753,0.00009418568,0.0003389359,0.00009591375,0.00004706407],"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":[0.000004210468,0.00006232602,0.0005365877,0.00000318299,0.00001523261,2.460743e-7,0.00004265284,0.0000130941,0.0003289172,0.9951714,0.0002868546,0.003535259],"study_design_scores_gemma":[0.0001874345,0.00001608246,0.0000570538,0.000008111936,0.000009827181,7.167368e-7,0.0002208048,0.0001393917,0.001034762,0.9659231,0.03232995,0.00007275878],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8550847,0.0002539732,0.02409424,0.001783372,0.0007617407,0.0006799963,0.00003776142,0.00009153633,0.1172127],"genre_scores_gemma":[0.9966896,0.00001620422,0.001090182,0.00001307491,0.00001730026,0.00004673511,0.000005029006,0.00001135418,0.002110573],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1416048,"threshold_uncertainty_score":0.249089,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01309379530485635,"score_gpt":0.3014985306486644,"score_spread":0.2884047353438081,"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."}}