#OEIS proofs
This collection gives self-contained proofs for formulas and interpretations recorded, or formerly conjectured, in the On-Line Encyclopedia of Integer Sequences. Each sequence has its own page so that OEIS entries can link to a stable proof.
A152947: unit interval cographs. We classify the connected natural unit interval graphs which are cographs and derive both their enumeration and the generating function for disconnected ones.
A189912: a binomial-sum identity. We split the defining sum by parity and reduce it to a known Catalan-triangle expression.
A358628: column formulas and Ehrhart–Legendre structure. We prove the conjectured column generating function and polynomial factorization, then derive an Ehrhart model, reciprocity, and real-rooted \(h^*\)-polynomials.