{"id":"W2407498472","doi":"","title":"On The Generalized Fibonacci And Pell Sequences By Hessenberg Matrices.","year":2010,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":26,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Fibonacci number; Mathematics; Recurrence relation; Combinatorics; Pisano period; Lucas sequence; Lucas number; Sequence (biology); Fibonacci polynomials; Prime (order theory); Discrete mathematics; Arithmetic; Orthogonal 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":[0.0005022149,0.0006448682,0.0003177974,0.001299269,0.0006969181,0.001418613,0.0004330072,0.0006435369,0.01111671],"category_scores_gemma":[0.002751547,0.0002271594,0.0003837206,0.00139159,0.001991989,0.003208932,0.0009018252,0.000987967,0.001859003],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00074197,"about_ca_system_score_gemma":0.0005761434,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009056351,"about_ca_topic_score_gemma":0.001018661,"domain_scores_codex":[0.9996934,0.00007982937,0.00001601189,0.00005792659,0.00009187954,0.00006104035],"domain_scores_gemma":[0.9994071,0.0002759224,0.0001118384,0.0000539228,0.000095239,0.00005605624],"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":[0.000005344982,0.000002971397,0.00005738128,0.00002376256,0.000001361765,0.00003218807,0.00006099229,0.001442707,0.0002860046,0.9883822,0.001009058,0.008696062],"study_design_scores_gemma":[0.000003479431,0.00001739394,0.0001482356,0.00001345782,0.000002191265,0.0001349644,0.00004145206,0.005942433,0.0004680874,0.9789743,0.01424335,0.00001066284],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1488221,0.01447005,0.5634537,0.002711745,0.0022305,0.0001551516,0.0007227422,0.0003940024,0.2670399],"genre_scores_gemma":[0.7646194,0.01299758,0.09917317,0.0009688492,0.002137359,0.0002117929,0.00063762,0.0001813839,0.1190729],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01111671,"threshold_uncertainty_score":0.03718913,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006300082100492631,"score_gpt":0.2459441925894685,"score_spread":0.2396441104889759,"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."}}