{"id":"W2399458915","doi":"","title":"Combinatorial Sums of Generalized Fibonacci and Lucas Numbers.","year":2011,"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":"Fibonacci number; Mathematics; Lucas number; Fibonacci polynomials; Pisano period; Lucas sequence; Combinatorics; Discrete mathematics; Classical orthogonal polynomials; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00008418653,0.0001220618,0.0002323959,0.00001915826,0.00008024301,0.000009939659,0.0001306385,0.00003467557,0.0004509629],"category_scores_gemma":[0.000009115721,0.0001128055,0.0000618374,0.0001147409,0.0001166881,0.0000840537,0.0000796071,0.00008306804,0.0000169559],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000662868,"about_ca_system_score_gemma":0.00001611995,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001052006,"about_ca_topic_score_gemma":2.898019e-7,"domain_scores_codex":[0.9993205,0.00001828072,0.0002305372,0.0001675336,0.00009422848,0.0001689017],"domain_scores_gemma":[0.9994057,0.00007572107,0.000112954,0.0002559407,0.00006205969,0.00008756854],"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":[0.00001552089,0.0001373938,0.002867043,0.00001025777,0.00003210409,2.694494e-7,0.0002907367,1.536863e-7,0.0004023406,0.9954153,0.0001802452,0.0006486523],"study_design_scores_gemma":[0.000902714,0.00004083087,0.000401792,0.000009893882,0.00002398116,4.557554e-7,0.0001720451,0.00001727267,0.01115211,0.9859333,0.001221683,0.0001239156],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9320061,0.00004035085,0.00103986,0.00003094234,0.0005133901,0.0002164447,0.00001845227,0.00003170386,0.06610275],"genre_scores_gemma":[0.9979298,0.000004383122,0.001828749,0.00001081305,0.00001929998,0.00003742623,0.00000932676,0.00001601665,0.0001441809],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06595857,"threshold_uncertainty_score":0.4937727,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01651732858689968,"score_gpt":0.2554035409633889,"score_spread":0.2388862123764892,"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."}}