SeqKind

Which linear recurrence a _Sequence denotes.

Every case is x(k) = p*x(k-1) + q*x(k-2) with its own seeds and coefficients, so there is one definition of the recurrence and the named variants are spellings of it:

An enum-tagged node rather than parse-time aliases, which is the _Statistic/StatKind and _Comparison/CompareOp pattern. Desugaring lucas(n) into fib(n, 2, 1) — the dfact -> mfact route — would have been cheaper, but the sugar is lost on the way back: the user types lucas(10) and the REPL, and :save, answer fib(10, 2, 1). Acceptable for dfact; self-defeating for a family whose point is that the names are related. This way each name survives the round trip and the equivalence (lucas(n) = fib(n, 2, 1)) is a documented fact rather than a second implementation.