{"id":"W1561862754","doi":"10.37236/2796","title":"Generalized Alcuin's Sequence","year":2012,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Mathematics; Integer (computer science); Sequence (biology); Modulo; Generating function; Function (biology); Discrete mathematics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001877212,0.0001580097,0.0003454775,0.00006997395,0.0001067273,0.00002933739,0.0005489409,0.0000583459,0.00005848227],"category_scores_gemma":[0.0008557063,0.0000992132,0.0001642701,0.0002456104,0.00009857057,0.000419389,0.00006871441,0.0006146129,0.00002766042],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003631296,"about_ca_system_score_gemma":0.0001663715,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001386013,"about_ca_topic_score_gemma":8.878513e-7,"domain_scores_codex":[0.9979887,0.0001546924,0.0005242623,0.00006038283,0.0005320937,0.0007398701],"domain_scores_gemma":[0.9980932,0.0007117152,0.0005410305,0.0003147228,0.0002245511,0.0001148091],"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":[0.00001434224,0.0001374535,0.00004870485,0.00002547479,0.00007106551,0.000002526019,0.0004208139,0.000003538,0.0005240073,0.9970807,0.001619046,0.00005229327],"study_design_scores_gemma":[0.0004567617,0.0001196175,0.00001283064,0.00002803601,0.0001109916,0.0003679322,0.0001853068,0.00002247231,0.003305912,0.9910018,0.004272356,0.000116022],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8741824,0.01129947,0.1037116,0.001474036,0.00161447,0.000353568,0.000001576355,0.00008800043,0.007274918],"genre_scores_gemma":[0.9955906,0.0005230861,0.0006881595,0.00005790479,0.0002524666,0.000002906707,1.887431e-7,0.00003270939,0.002852015],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1214082,"threshold_uncertainty_score":0.4045797,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05783539937336117,"score_gpt":0.3442194959542728,"score_spread":0.2863840965809116,"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."}}