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# Tribonacci

> Compute the nth [Tribonacci number][tribonacci-number].

<section class="intro">

The [Tribonacci numbers][tribonacci-number] are the integer sequence

<!-- <equation class="equation" label="eq:tribonacci_sequence" align="center" raw="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" alt="Tribonacci sequence"> -->

<div class="equation" align="center" data-raw-text="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" data-equation="eq:tribonacci_sequence">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_sequence.svg" alt="Tribonacci sequence">
    <br>
</div> -->

<!-- </equation> -->

The sequence is defined by the recurrence relation

<!-- <equation class="equation" label="eq:tribonacci_recurrence_relation" align="center" raw="F_n = F_{n-1} + F_{n-2} + F_{n-3}" alt="Tribonacci sequence recurrence relation"> -->

<!-- <div class="equation" align="center" data-raw-text="F_n = F_{n-1} + F_{n-2} + F_{n-3}" data-equation="eq:tribonacci_recurrence_relation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_recurrence_relation.svg" alt="Tribonacci sequence recurrence relation">
    <br>
</div>

<!-- </equation> -->

with seed values `F_0 = 0`, `F_1 = 0`, and `F_2 = 1`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var tribonacci = require( '@stdlib/math/base/special/tribonacci' );
```

#### tribonacci( n )

Computes the nth [Tribonacci number][tribonacci-number].

```javascript
var v = tribonacci( 0 );
// returns 0

v = tribonacci( 1 );
// returns 0

v = tribonacci( 2 );
// returns 1

v = tribonacci( 3 );
// returns 1

v = tribonacci( 63 );
// returns 8607945812375585
```

If `n > 63`, the function returns `NaN`, as larger [Tribonacci numbers][tribonacci-number] cannot be safely represented in [double-precision floating-point format][ieee754].

```javascript
var v = tribonacci( 64 );
// returns NaN
```

If not provided a nonnegative integer value, the function returns `NaN`.

```javascript
var v = tribonacci( 3.14 );
// returns NaN

v = tribonacci( -1 );
// returns NaN
```

If provided `NaN`, the function returns `NaN`.

```javascript
var v = tribonacci( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var tribonacci = require( '@stdlib/math/base/special/tribonacci' );

var v;
var i;

for ( i = 0; i < 64; i++ ) {
    v = tribonacci( i );
    console.log( v );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/tribonacci.h"
```

#### stdlib_base_tribonacci( n )

Computes the nth [Tribonacci number][tribonacci-number].

```c
double out = stdlib_base_tribonacci( 0 );
// returns 0

out = stdlib_base_tribonacci( 1 );
// returns 0
```

The function accepts the following arguments:

-   **n**: `[in] int32_t` input value.

```c
double stdlib_base_tribonacci( const int32_t n );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/tribonacci.h"
#include <stdio.h>
#include <stdint.h>

int main( void ) {
    int32_t i;
    double v;

    for ( i = 0; i < 64; i++ ) {
        v = stdlib_base_tribonacci( i );
        printf( "tribonacci(%d) = %lf\n", i, v );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math/base/special/fibonacci`][@stdlib/math/base/special/fibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Fibonacci number.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[tribonacci-number]: https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

<!-- <related-links> -->

[@stdlib/math/base/special/fibonacci]: https://github.com/stdlib-js/math/tree/main/base/special/fibonacci

<!-- </related-links> -->

</section>

<!-- /.links -->
