Negafibonacci Numbers Generator

Every schoolbook stops at zero when it draws the Fibonacci sequence, but the recurrence F(n) = F(n-1) + F(n-2) holds the same 1, 1, 2, 3, 5, 8, 13 pattern on the other side of the axis. Run it backwards and a stranger, signed mirror appears: 13, -8, 5, -3, 2, -1, 1, 0. The absolute values are the familiar Fibonacci numbers, and the signs alternate by the identity F(-n) = (-1)^(n+1)·F(n) — a compact rule that generates the entire negative half exactly.

Negafibonacci Numbers Generator computes the extended sequence for any integer index range, from -20 to 20 up to -10,000 to 10,000. Every term uses exact BigInt arithmetic, rows show index and value, a summary proves that symmetric ranges sum to zero, and the output downloads or copies in one click. A reference tab documents the identity, the sign rule and the first negative terms. Everything runs in your browser; nothing is uploaded.

• True negative indexes: F(-1) through F(-10,000) and back, all via the exact recurrence rule.
• Any range: Start and end indexes are both free — negative, zero or positive — up to 10,001 terms.
• Exact BigInt values: A 2,000-digit term renders exactly, no rounding, no scientific notation.
• Sign identity: F(-n) = (-1)^(n+1)·F(n) applied at every index, alternating signs on even n.
• Zero-sum proof: The summary line totals the whole range, showing symmetric runs cancel exactly.
• Term count control: Ranges beyond 10,001 terms are clamped with a clear message instead of failing.
• Copy or download: Values-only list, one per line, ready for spreadsheets and worksheets.
• Reference tab: The identity, sign rules and the first ten negative terms side by side.
• Free and private: Everything runs locally in the browser; nothing is uploaded or stored.

1. Set the start index — a negative, zero or positive integer, for example -10.
2. Set the end index — for example 10, generating F(-10) through F(10) in order.
3. Read the rows — each index is paired with its exact value; negative indexes alternate signs.
4. Check the summary — term count and the total of the range, proving symmetric runs cancel to zero.
5. Copy or download the values-only list for worksheets, tests or analysis.

Example 1 — The anchor block. Set -5 to 5. The output is 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5 — eleven terms that show both the sign alternation and the classic positives meeting at zero.

Example 2 — A self-check. Generate -2 to 2: -1, 1, 0, 1, 1. The extended side reproduces the identity F(-2) = -1 and F(-1) = 1 exactly.

Example 3 — Cancellation. Generate -6 to 6. The terms -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8 total exactly 0, as the summary line reports.

Example 4 — A big symmetric range. Generate -50 to 50. The tool computes 101 exact values in milliseconds, all in BigInt, and the total is still exactly zero.

Example 5 — Pure positive. Set 1 to 12 to get the familiar 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 — the classic sequence, available from the same generator.

• The missing half of Fibonacci: Negative indexes are rarely taught and never hand-computed — one click produces them all.
• Exact at every size: BigInt arithmetic renders 2,000-digit terms without a single rounding error.
• Range freedom: Start and end are both free, with a hard 10,001-term safety cap.
• Verifiable output: The symmetric-zero total and the sign identity give every run a built-in proof.
• Classroom ready: Copyable lists feed worksheets, quizzes and combinatorics sessions directly.
• Private and free: Computation happens entirely in the browser; nothing is uploaded, stored or logged.