# Fibonacci sequence

`fibonacci-sequence` · version 1.0.0 · Numbers & math · free, no key needed

List exact Fibonacci numbers for an inclusive zero-based index range as decimal strings.

**Use when you need to: list fibonacci numbers · fibonacci sequence range · fibonacci numbers between indices.**

## Decide before calling

Read the [versioned contract](/v1/tools/fibonacci-sequence/versions/1.0.0) and the supported scope below. Reuse `fibonacci-sequence@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `fibonacci-sequence@1.0.0` for list fibonacci numbers. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- list fibonacci numbers
- fibonacci sequence range
- fibonacci numbers between indices
- generate first fibonacci values
- bounded fibonacci sequence
- fibonacci list from index to index
- exact fibonacci series

## Not supported

- unbounded Fibonacci streams
- Lucas number ranges
- negative or fractional indices

## Behavior

- The inclusive range returns F(start_index) through F(end_index), where F(0)=0 and F(1)=1.
- Ranges contain 1 through 100 items; values are unsigned base-10 strings in ascending index order.
- Standard version: OEIS A000045 (live entry retrieved 2026-11-05; NAME, initial terms, OFFSET 0,4); stable source URL: https://oeis.org/A000045.

## Input

- `start_index` (integer, required): min 0; max 5000
- `end_index` (integer, required): min 0; max 5000

## Output

- `start_index` (integer, required): min 0; max 5000
- `end_index` (integer, required): min 0; max 5000
- `values` (array of string, required): min items 1; max items 100; each min length 1; each max length 1045; each pattern `^[0-9]+$`
- `standard_version` (string, required): min length 1; max length 120

## Limits

- max input bytes: 96
- max index: 5000
- max items: 100
- max digits per item: 1045
- max iterations: 1400
- max output bytes: 112000

## Example

Request input:

```json
{
  "start_index": 0,
  "end_index": 7
}
```

Response:

```json
{
  "result": {
    "start_index": 0,
    "end_index": 7,
    "values": [
      "0",
      "1",
      "1",
      "2",
      "3",
      "5",
      "8",
      "13"
    ],
    "standard_version": "OEIS A000045 (live entry retrieved 2026-11-05; NAME, initial terms, OFFSET 0,4)"
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "fibonacci-sequence",
  "version": "1.0.0",
  "input": {
    "start_index": 0,
    "end_index": 7
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/fibonacci-sequence/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"start_index":0,"end_index":7}'
```

The machine-readable contract is at [/v1/tools/fibonacci-sequence/versions/1.0.0](/v1/tools/fibonacci-sequence/versions/1.0.0).

### CLI

```sh
node cli.mjs run fibonacci-sequence 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Correlation spearman](/tools/correlation-spearman): Compute Spearman rank correlation with average ranks for ties and return a rounded decimal coefficient.
- [Correlation kendall tau](/tools/correlation-kendall-tau): Compute Kendall tau-b correlation with tie correction and return a precision-rounded decimal coefficient.
- [Fibonacci number](/tools/fibonacci-number): Compute the Fibonacci number at a zero-based index and return its exact decimal string.
- [Lucas number](/tools/lucas-number): Compute the Lucas number at a zero-based index and return its exact decimal string.
- [Permutation indices check](/tools/permutation-indices-check): Check whether claimed indices are exactly one occurrence of every source index, reporting the first discrepancy.
- [Sample summary check](/tools/sample-summary-check): Check claimed count, sum, mean, median, range, variance or SD of an exact sample; returns the first mismatching field.