A Fibonacci (rabbit sequence) calculator covering three common jobs in one box, one entry per line.

How to use:
1. Pick a mode:
   - Nth term: one index per line, e.g. 100 (indexing starts at F(0)=0);
   - First N terms: one count per line, e.g. 20, printing F(0) to F(N-1);
   - Index range: one range per line, e.g. 10,20; reversed endpoints are swapped automatically;
2. Optionally switch the sequence to Fibonacci F(n) or Lucas L(n) (L(0)=2, L(1)=1) - both share the same input;
3. Hit Run to get the index, value and digit count for each entry, then copy the result or export it as CSV.

Under the hood it uses fast doubling - F(2k) = F(k) x (2F(k+1) - F(k)) and F(2k+1) = F(k)^2 + F(k+1)^2 - so it needs only O(log n) big-integer multiplications. That is why a 21-digit value like F(100) = 354224848179261915075, or the full 209 digits of F(1000), come back exactly instead of losing precision the way float-based implementations do. Indices go up to 10000 (about 2090 digits) and a single run can output up to 500 terms.