time-to-botec/squiggle/node_modules/@stdlib/math/iter/sequences/squared-triangular/README.md

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# iterSquaredTriangularSeq

> Create an iterator which generates a sequence of [squared triangular numbers][oeis-a000537].

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<section class="intro">

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

<!-- <equation class="equation" label="eq:squared_triangular_numbers_sequence" align="center" raw="0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, \ldots" alt="Triangular number sequence"> -->

<div class="equation" align="center" data-raw-text="0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, \ldots" data-equation="eq:squared_triangular_numbers_sequence">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@ffa1a1acab2d2c9973d3ad22a5dfc25afd86767a/lib/node_modules/@stdlib/math/iter/sequences/squared-triangular/docs/img/equation_squared_triangular_numbers_sequence.svg" alt="Triangular number sequence">
    <br>
</div>

<!-- </equation> -->

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

[Triangular numbers][@stdlib/math/iter/sequences/triangular] 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@ffa1a1acab2d2c9973d3ad22a5dfc25afd86767a/lib/node_modules/@stdlib/math/iter/sequences/squared-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.

The nth [squared triangular number][squared-triangular-number] is the nth [triangular number][@stdlib/math/iter/sequences/triangular] squared.

</section>

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<!-- Package usage documentation. -->

<section class="usage">

## Usage

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

#### iterSquaredTriangularSeq( \[options] )

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

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

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

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

v = it.next().value;
// returns 9

v = it.next().value;
// returns 36

v = it.next().value;
// returns 100

// ...
```

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: `11585`.

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 = iterSquaredTriangularSeq( 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>

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<!-- Package usage examples. -->

<section class="examples">

## Examples

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

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

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

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<section class="links">

[oeis-a000537]: https://oeis.org/A000537

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

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

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

</section>

<!-- /.links -->