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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.02613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-09T02:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"55bf094b82fc78e40d8d67d5ab93b8653fa087b7b5eda0c185ec9a4591732483","abstract_canon_sha256":"adf3e4006ac45912c97d78afc9dfa4b36a791a0fe41ae408e100a6d53db8bcb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:34.574646Z","signature_b64":"Ty6b9dgKMNsaHKC52H1vo/M9FqzuPncXZyGkWzeoTbZ4HKr+5bSePRBJvuFgqn0epoeASfkDfjLQeMClc+WDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a213ce1dc09242946d5a412e7dc64f593135f991f7873974b58cdd62ea0db09e","last_reissued_at":"2026-05-18T01:33:34.573957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:34.573957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.02613","created_at":"2026-05-18T01:33:34.574053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02613v1","created_at":"2026-05-18T01:33:34.574053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02613","created_at":"2026-05-18T01:33:34.574053+00:00"},{"alias_kind":"pith_short_12","alias_value":"UIJ44HOASJBJ","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UIJ44HOASJBJI3K2","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UIJ44HOA","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE","json":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE.json","graph_json":"https://pith.science/api/pith-number/UIJ44HOASJBJI3K2IEXH3RSPLE/graph.json","events_json":"https://pith.science/api/pith-number/UIJ44HOASJBJI3K2IEXH3RSPLE/events.json","paper":"https://pith.science/paper/UIJ44HOA"},"agent_actions":{"view_html":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE","download_json":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE.json","view_paper":"https://pith.science/paper/UIJ44HOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02613&json=true","fetch_graph":"https://pith.science/api/pith-number/UIJ44HOASJBJI3K2IEXH3RSPLE/graph.json","fetch_events":"https://pith.science/api/pith-number/UIJ44HOASJBJI3K2IEXH3RSPLE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE/action/storage_attestation","attest_author":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE/action/author_attestation","sign_citation":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE/action/citation_signature","submit_replication":"https://pith.science/pith/UIJ44HOASJBJI3K2IEXH3RSPLE/action/replication_record"}},"created_at":"2026-05-18T01:33:34.574053+00:00","updated_at":"2026-05-18T01:33:34.574053+00:00"}