{"paper":{"title":"On nearly linear recurrence sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NT","authors_text":"Attila Peth\\H{o}, Jan-Hendrik Evertse, Shigeki Akiyama","submitted_at":"2016-07-29T20:40:38Z","abstract_excerpt":"A nearly linear recurrence sequence (nlrs) is a complex sequence $(a_n)$ with the property that there exist complex numbers $A_0$,$\\ldots$, $A_{d-1}$ such that the sequence $\\big(a_{n+d}+A_{d-1}a_{n+d-1}+\\cdots +A_0a_n\\big)_{n=0}^{\\infty}$ is bounded. We give an asymptotic Binet-type formula for such sequences. We compare $(a_n)$ with a natural linear recurrence sequence (lrs) $(\\tilde{a}_n)$ associated with it and prove under certain assumptions that the difference sequence $(a_n- \\tilde{a}_n)$ tends to infinity. We show that several finiteness results for lrs, in particular the Skolem-Mahler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00024","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"}