{"id":"recurrence-relation","domain":"discrete","type":"Concept","title":"Recurrence Relation","slug":"recurrence-relation","url":"/mathematics/discrete/recurrence-relation/","summary":"Defines sequence terms using previous terms. Fibonacci is the classic example. Solvable via characteristic equations, generating functions, Master Theorem.","formal_definition":"Fn = Fn-1 + Fn-2, F1=1, F2=1 (Fibonacci example)","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Graham, R.L., Knuth, D.E. and Patashnik, O. (1994). Concrete Mathematics. 2nd ed."},{"tier":1,"citation":"Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2022). Introduction to Algorithms. 4th ed."},{"tier":2,"citation":"Plofker, K. (2009). Mathematics in India. Princeton University Press."},{"tier":3,"citation":"Posamentier, A.S. and Lehmann, I. (2007). The Fabulous Fibonacci Numbers. Prometheus Books."}],"relationships":[{"type":"related_to","target":"golden-ratio","label":"Golden Ratio — Binet's formula"},{"type":"used_in","target":"big-o-notation","label":"Big-O Notation — algorithm analysis"},{"type":"instance_in","target":"tower-of-hanoi","label":"Tower of Hanoi"},{"type":"uses","target":"combinatorics","label":"Combinatorics — generating functions"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.1"}