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https://github.com/stdlib-js/math-base-special-lucas
Compute the nth Lucas number.
https://github.com/stdlib-js/math-base-special-lucas
fib fibonacci function integer javascript lucas math mathematics node node-js nodejs number sequences special special-functions stdlib
Last synced: 17 days ago
JSON representation
Compute the nth Lucas number.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-special-lucas
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-14T16:37:44.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-10-01T15:02:52.000Z (about 1 month ago)
- Last Synced: 2024-10-04T22:17:21.618Z (about 1 month ago)
- Topics: fib, fibonacci, function, integer, javascript, lucas, math, mathematics, node, node-js, nodejs, number, sequences, special, special-functions, stdlib
- Language: Python
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 442 KB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
Awesome Lists containing this project
README
About stdlib...
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To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
# Lucas
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Compute the nth [Lucas number][lucas-number].
The [Lucas numbers][lucas-number] are the integer sequence
```math
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, \ldots
```
The sequence is defined by the recurrence relation
```math
L_n = \begin{cases}2 & \textrm{if}\ n = 0\\1 & \textrm{if}\ n = 1\\L_{n-1} + L_{n-2} & \textrm{if}\ n > 1\end{cases}
```
## Installation
```bash
npm install @stdlib/math-base-special-lucas
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var lucas = require( '@stdlib/math-base-special-lucas' );
```
#### lucas( n )
Computes the nth [Lucas number][lucas-number].
```javascript
var v = lucas( 0 );
// returns 2
v = lucas( 1 );
// returns 1
v = lucas( 2 );
// returns 3
v = lucas( 3 );
// returns 4
v = lucas( 76 );
// returns 7639424778862807
```
If `n > 76`, the function returns `NaN`, as larger [Lucas numbers][lucas-number] cannot be safely represented in [double-precision floating-point format][ieee754].
```javascript
var v = lucas( 77 );
// returns NaN
```
If not provided a nonnegative integer value, the function returns `NaN`.
```javascript
var v = lucas( 3.14 );
// returns NaN
v = lucas( -1 );
// returns NaN
```
If provided `NaN`, the function returns `NaN`.
```javascript
var v = lucas( NaN );
// returns NaN
```
## Examples
```javascript
var lucas = require( '@stdlib/math-base-special-lucas' );
var v;
var i;
for ( i = 0; i < 77; i++ ) {
v = lucas( i );
console.log( v );
}
```
* * *
## C APIs
### Usage
```c
#include "stdlib/math/base/special/lucas.h"
```
#### stdlib_base_lucas( n )
Computes the nth [Lucas number][lucas-number].
```c
double out = stdlib_base_lucas( 0 );
// returns 2
out = stdlib_base_lucas( 1 );
// returns 1
```
The function accepts the following arguments:
- **n**: `[in] int32_t` input value.
```c
double stdlib_base_lucas( const int32_t n );
```
### Examples
```c
#include "stdlib/math/base/special/lucas.h"
#include
#include
int main( void ) {
int32_t i;
double v;
for ( i = 0; i < 77; i++ ) {
v = stdlib_base_lucas( i );
printf( "lucas(%d) = %lf\n", i, v );
}
}
```
* * *
## See Also
- [`@stdlib/math-base/special/fibonacci`][@stdlib/math/base/special/fibonacci]: compute the nth Fibonacci number.
- [`@stdlib/math-base/special/negalucas`][@stdlib/math/base/special/negalucas]: compute the nth negaLucas number.
* * *
## Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-lucas.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-lucas
[test-image]: https://github.com/stdlib-js/math-base-special-lucas/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-special-lucas/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-lucas/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-lucas?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-lucas/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-lucas/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-lucas/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-lucas/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-lucas/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-lucas/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-lucas/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-lucas/main/LICENSE
[lucas-number]: https://en.wikipedia.org/wiki/Lucas_number
[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
[@stdlib/math/base/special/fibonacci]: https://github.com/stdlib-js/math-base-special-fibonacci
[@stdlib/math/base/special/negalucas]: https://github.com/stdlib-js/math-base-special-negalucas