{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005236501,0.0006898794,0.0007871272,0.003189245,0.001916056,0.0032977,0.0008652288,0.0009517777,0.01006536],"category_scores_gemma":[0.003340122,0.0004208488,0.000670857,0.001744054,0.001953556,0.003474085,0.001472667,0.001277945,0.001602954],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001118547,"about_ca_system_score_gemma":0.0005705514,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009115374,"about_ca_topic_score_gemma":0.002190073,"domain_scores_codex":[0.99939,0.0001465145,0.00003670748,0.00008560692,0.0002492966,0.00009177811],"domain_scores_gemma":[0.9990665,0.0003877033,0.000128397,0.0001028229,0.0002041951,0.0001103692],"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":[0.00001533318,0.000005219007,0.0001147335,0.00003433902,0.000005271933,0.00007027674,0.00006182108,0.0004260194,0.0004095768,0.9909044,0.00195423,0.005998869],"study_design_scores_gemma":[0.000006079845,0.000007373118,0.000253762,0.00001898858,0.000009459069,0.0002962684,0.00005789532,0.002966804,0.0002911208,0.9879926,0.008086643,0.0000129652],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3554009,0.01259429,0.1629849,0.00273939,0.002162325,0.0001134739,0.000943487,0.000599218,0.462462],"genre_scores_gemma":[0.8928819,0.002356875,0.04427392,0.0006344412,0.00119853,0.0001487385,0.0005493598,0.0001794548,0.05777675],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01006536,"threshold_uncertainty_score":0.03367192,"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."}}