{"paper":{"title":"Nested Recurrence Relations With Conolly-Like Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abraham Isgur, Alejandro Erickson, Bradley W. Jackson, Frank Ruskey, Stephen M. Tanny","submitted_at":"2015-09-09T02:42:46Z","abstract_excerpt":"A nondecreasing sequence of positive integers is $(\\alpha,\\beta)$-Conolly, or Conolly-like for short, if for every positive integer $m$ the number of times that $m$ occurs in the sequence is $\\alpha + \\beta r_m$, where $r_m$ is $1$ plus the 2-adic valuation of $m$. A recurrence relation is $(\\alpha, \\beta)$-Conolly if it has an $(\\alpha, \\beta)$-Conolly solution sequence. We discover that Conolly-like sequences often appear as solutions to nested (or meta-Fibonacci) recurrence relations of the form $A(n) = \\sum_{i=1}^k A(n-s_i-\\sum_{j=1}^{p_i} A(n-a_{ij}))$ with appropriate initial conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02613","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}