Overview
The Fibonacci Generator API computes Fibonacci sequence values along with derived statistics — a sum, the trailing 5 consecutive-value ratios, and the most recent ratio as an approximation of the golden ratio. It accepts two mutually-exclusive modes: `count` for a fixed-length response, or `maxvalue` for every Fibonacci number up to a numeric ceiling. An optional `startfrom` parameter advances the generator before emission begins. All arithmetic uses standard JavaScript Number type on the server, so values above Number.MAX_SAFE_INTEGER (around the 79th Fibonacci number) cannot be represented exactly — the precision ceiling is end-to-end. The ratios array is always truncated to the last 5 entries regardless of sequence length, and each ratio is rounded to 6 decimal places.
Live Test Fibonacci Sequence Source →
Formula
One function covers the whole catalog: the first argument names the source, the rest are its inputs, and the "field" pair says which single value lands in the cell. Formulas covers the grammar that applies to all of them.
=VERVE("fibonaccigenerator", A2, "field", "start_from")=VERVE.CALL("fibonaccigenerator", A2, "field", "start_from")A2 holds the count you are looking up. Drag the formula down and each row resolves on its own.
With literal values
Nothing has to come from a cell — typed values work the same way.
=VERVE("fibonaccigenerator", 10, "field", "start_from")=VERVE.CALL("fibonaccigenerator", 10, "field", "start_from")Inputs
Required inputs are positional, in the order below. Everything else is passed as a "name", value pair after them — the same shape as SUMIFS. Premium inputs are accepted on every plan but only take effect on plans that include them.
| Input | Type | Where it goes | Description |
|---|---|---|---|
countRequired | integer | argument 2 (A2) | Number of Fibonacci numbers to generate range 1–1000 |
startfromOptional | integer | "startfrom", value | Start from this position in the sequence range 0–∞ |
Passing an option
=VERVE("fibonaccigenerator", A2, "startfrom", 0)=VERVE.CALL("fibonaccigenerator", A2, "startfrom", 0)What lands in your sheet
The "field" pair is what makes the formula resolve to one cell. Its value is a dot-path from the table below, so swapping it is how you pull a different value — one formula per column.
Seeing everything at once
Drop the "field" pair and the formula returns the whole response instead: two columns, field name on the left and value on the right, spilling from the cell you typed in.
=VERVE("fibonaccigenerator", A2)=VERVE.CALL("fibonaccigenerator", A2)The second row's table would land on top of the first's, and every cell after the first reads #REF! (#SPILL! in Excel). Keep one per sheet, or name a field, and leave the cells below and to the right empty.
Response fields
Paths are relative to data. Each one is exactly what the "field" pair accepts, so swapping it is how you pull a different value into a cell. On a plan without a Premium field the cell reads #PREMIUM(field) rather than a value, so a locked field never looks like a real answer.
| Use as "field" | Type | Example cell value | Description |
|---|---|---|---|
sequence | array | [0,1,1] | Array of generated Fibonacci numbers Length is determined server-side based on maxvalue, not by the caller. May be empty when startfrom advances past maxvalue. |
count | number | 10 | Total count of Fibonacci numbers generated |
start_from | number | 0 | Starting position in the Fibonacci sequence |
first_value | number | 0 | First value in the generated sequence |
last_value | number | 34 | Last value in the generated sequence |
sum | number | 88 | Sum of all numbers in the sequence |
ratios | array | [1.666667,1.6,1.625] | Array of ratios between consecutive sequence values Only the last 5 ratios are returned. Same skip rule for zero denominators. Each value rounded to 6 decimal places. |
golden_ratio_approximation | number | 1.619048 | Approximation of golden ratio from sequence ratios Returns null when no ratios could be computed. |
Filling a whole column
Both platforms make one batched call for a column rather than one request per cell, and both cost the same — 2 credits per row looked up. How you write it differs, because the two runtimes batch at different points.
=VERVE("fibonaccigenerator", A2:A100, "field", "start_from")In Google Sheets, give the arguments ranges and the answers spill down from the cell you typed in. Custom functions there run synchronously and in isolation, so dragged cells cannot be coalesced — the range form is how a column becomes one call. The "field" pair is required here: a per-row two-column table has nowhere to spill. Use a full column per input (A2:A100, not A2) — a single-cell reference is read as row 1 only and the rest of the column comes back blank.
In Excel, type the formula once and fill down — no range form and none needed, because its runtime is asynchronous and the add-in coalesces the calls a fill produces into a single batched request. Do not hand VERVE.CALL a range: Excel flattens it into positional arguments, so A2:A100 arrives as a hundred separate arguments and the cell reads #ERR rather than filling.
Either way, column A holds your count values and the answers land beside them, one row each, blank rows skipped.
When a cell doesn't fill
A failed lookup returns readable text starting with #ERR rather than a spreadsheet error, because Excel cannot show a custom message on a real error — you would get a bare #VALUE! with no reason. The trade-off is that IFERROR() will not catch it; test with LEFT(cell, 4) = "#ERR" instead. Error handling covers the rest.
| Cell reads | What happened |
|---|---|
#ERR Not connected | No API key saved. Open the side panel and connect your account. |
#ERR Replace <name> with a cell or value | A preview formula was copied as-is. Swap the placeholder for a cell reference. |
#ERR No "x" in fibonaccigenerator | An option name this source does not take. The message lists the ones it does. |
#ERR No data point "…" | The "field" path is not in the response. Check it against the table above. |
#PREMIUM(field) | The field exists but your plan does not include it. |
#ERR Out of credits | The cycle's credits are spent. Usage resets on your billing date. |
Before the formula works
The add-in reads the API key you saved once in the side panel — the key never goes in the formula, so a shared sheet does not leak it and a collaborator without access simply sees the last calculated values.
- Install the add-in for Google Sheets or Excel.
- Open the side panel and sign in, or paste a key from your dashboard.
- Type the formula above into any cell.
Use cases
- Math Education
- Teach Fibonacci sequences and golden ratio concepts in educational applications and tools
- Algorithm Testing
- Generate test data for algorithms and performance testing using Fibonacci sequences
- Visual Design
- Apply Fibonacci ratios and golden ratio proportions in design and layout calculations
- Data Analysis
- Use Fibonacci numbers in technical analysis, trading algorithms, and pattern recognition
Other ways to use Fibonacci Sequence
Set up Fibonacci Sequence on VerveSheets, or reach the same source a different way. Your VerveSheets account and credits work on all of them — one key, one balance.
Related
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