npm package: @stdlib/math-iter-sequences-triangular
Description: Create an iterator which generates a sequence of triangular numbers.
Author: The Stdlib Authors
Latest version: 0.2.3

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# iterTriangularSeq

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Create an iterator which generates a sequence of [triangular numbers][oeis-a000217].

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<section class="intro">

The [triangular numbers][triangular-number] are the integer sequence

<!-- <equation class="equation" label="eq:triangular_numbers_sequence" align="center" raw="0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, \ldots" alt="Triangular number sequence"> -->

<div class="equation" align="center" data-raw-text="0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, \ldots" data-equation="eq:triangular_numbers_sequence">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7000a1b5cd08bb73f2dfe04976524042ab3b580d/lib/node_modules/@stdlib/math/iter/sequences/triangular/docs/img/equation_triangular_numbers_sequence.svg" alt="Triangular number sequence">
    <br>
</div> -->

<!-- </equation> -->

starting at the 0th [triangular number][triangular-number].

[Triangular numbers][triangular-number] are given by the following explicit formulas

<!-- <equation class="equation" label="eq:triangular_numbers" align="center" raw="T_n = \sum_{i=1}^{n} i = 1 + 2 + 3 + \ldots + n = \frac{n(n+1)}{2} = \binom{n+1}{2}" alt="Triangular number formulas"> -->

<!-- <div class="equation" align="center" data-raw-text="T_n = \sum_{i=1}^{n} i = 1 + 2 + 3 + \ldots + n = \frac{n(n+1)}{2} = \binom{n+1}{2}" data-equation="eq:triangular_numbers">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7000a1b5cd08bb73f2dfe04976524042ab3b580d/lib/node_modules/@stdlib/math/iter/sequences/triangular/docs/img/equation_triangular_numbers.svg" alt="Triangular number formulas">
    <br>
</div>

<!-- </equation> -->

where the last formula corresponds to a [binomial coefficient][@stdlib/math/base/special/binomcoef], representing the number of distinct pairs that can be selected from `n+1` items.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-iter-sequences-triangular
```

</section>

<section class="usage">

## Usage

```javascript
var iterTriangularSeq = require( '@stdlib/math-iter-sequences-triangular' );
```

#### iterTriangularSeq( \[options] )

Returns an iterator which generates a sequence of [triangular numbers][triangular-number].

```javascript
var it = iterTriangularSeq();
// returns <Object>

var v = it.next().value;
// returns 0

v = it.next().value;
// returns 1

v = it.next().value;
// returns 3

v = it.next().value;
// returns 6

v = it.next().value;
// returns 10

// ...
```

The returned iterator protocol-compliant object has the following properties:

-   **next**: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a `value` property and a `done` property having a `boolean` value indicating whether the iterator is finished.
-   **return**: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.

The function supports the following `options`:

-   **iter**: number of iterations. Default: `134217727`.

By default, the function returns a finite iterator to avoid exceeding the maximum safe double-precision floating-point integer. To adjust the number of iterations, set the `iter` option.

```javascript
var opts = {
    'iter': 2
};
var it = iterTriangularSeq( opts );
// returns <Object>

var v = it.next().value;
// returns 0

v = it.next().value;
// returns 1

var bool = it.next().done;
// returns true
```

</section>

<!-- /.usage -->

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

<section class="notes">

## Notes

-   If an environment supports `Symbol.iterator`, the returned iterator is iterable.

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

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

```javascript
var iterTriangularSeq = require( '@stdlib/math-iter-sequences-triangular' );

// Create an iterator:
var opts = {
    'iter': 100
};
var it = iterTriangularSeq( opts );

// Perform manual iteration...
var v;
while ( true ) {
    v = it.next();
    if ( v.done ) {
        break;
    }
    console.log( v.value );
}
```

</section>

<!-- /.examples -->

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<section class="references">

</section>

<!-- /.references -->

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<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-iter/sequences/squared-triangular`][@stdlib/math/iter/sequences/squared-triangular]</span><span class="delimiter">: </span><span class="description">create an iterator which generates a sequence of squared triangular numbers.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[oeis-a000217]: https://oeis.org/A000217

[triangular-number]: https://en.wikipedia.org/wiki/Triangular_number

[@stdlib/math/base/special/binomcoef]: https://www.npmjs.com/package/@stdlib/math-base-special-binomcoef

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[@stdlib/math/iter/sequences/squared-triangular]: https://www.npmjs.com/package/@stdlib/math-iter-sequences-squared-triangular

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