{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005546467,0.0005352392,0.0004536737,0.001434414,0.001045095,0.001088107,0.0008982726,0.0007936308,0.007731846],"category_scores_gemma":[0.002370619,0.0002237703,0.0004868871,0.001096405,0.001164968,0.001725658,0.001119786,0.001185833,0.001573529],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001314894,"about_ca_system_score_gemma":0.0006867042,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00181765,"about_ca_topic_score_gemma":0.00223092,"domain_scores_codex":[0.9992605,0.0001425455,0.00004220491,0.0001364232,0.0002173373,0.0002009137],"domain_scores_gemma":[0.9990007,0.0001781383,0.0001017089,0.0001618854,0.0003882529,0.0001693308],"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":[0.0001498151,0.00003085574,0.001042975,0.0001037874,0.00001151898,0.00032725,0.0003870123,0.00437605,0.008520064,0.9448442,0.003243177,0.03696328],"study_design_scores_gemma":[0.0000468589,0.0001339451,0.001377911,0.00009192954,0.0000202155,0.000950176,0.0002192826,0.07902879,0.01112894,0.8518262,0.05508882,0.00008693502],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4927041,0.002697605,0.3105575,0.001087416,0.0008001452,0.0001974267,0.0008917846,0.0009528594,0.1901113],"genre_scores_gemma":[0.8922281,0.0007141823,0.06367648,0.0006651993,0.0002130755,0.0002043012,0.0007774469,0.0002525101,0.04126875],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007731846,"threshold_uncertainty_score":0.02586561,"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."}}