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

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# iterNegaLucasSeq

> Create an iterator which generates a [negaLucas sequence][lucas-number].

<!-- 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">

The [negaLucas numbers][lucas-number] are the integer sequence

<!-- <equation class="equation" label="eq:negalucas_sequence" align="center" raw="2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, \ldots" alt="NegaLucas sequence"> -->

<div class="equation" align="center" data-raw-text="2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, \ldots" data-equation="eq:negalucas_sequence">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/negalucas/docs/img/equation_negalucas_sequence.svg" alt="NegaLucas sequence">
    <br>
</div>

<!-- </equation> -->

The sequence is defined by the recurrence relation

<!-- <equation class="equation" label="eq:negalucas_recurrence_relation" align="center" raw="L_{n-2} = L_{n} - L_{n-1}" alt="NegaLucas sequence recurrence relation"> -->

<div class="equation" align="center" data-raw-text="L_{n-2} = L_{n} - L_{n-1}" data-equation="eq:negalucas_recurrence_relation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/negalucas/docs/img/equation_negalucas_recurrence_relation.svg" alt="NegaLucas sequence recurrence relation">
    <br>
</div>

<!-- </equation> -->

which yields

<!-- <equation class="equation" label="eq:negalucas_lucas" align="center" raw="L_{-n} = (-1)^{n} L_n" alt="NegaLucas relationship to Lucas numbers"> -->

<div class="equation" align="center" data-raw-text="L_{-n} = (-1)^{n} L_n" data-equation="eq:negalucas_lucas">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/negalucas/docs/img/equation_negalucas_lucas.svg" alt="NegaLucas relationship to Lucas numbers">
    <br>
</div>

<!-- </equation> -->

with seed values `L_0 = 2` and `L_{-1} = -1`.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="usage">

## Usage

```javascript
var iterNegaLucasSeq = require( '@stdlib/math/iter/sequences/negalucas' );
```

#### iterNegaLucasSeq( \[options] )

Returns an iterator which generates a [negaLucas sequence][lucas-number].

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

var v = it.next().value;
// returns 2

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

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

// ...
```

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: `77`.

The returned iterator can only generate the first `77` [negaLucas numbers][lucas-number], as larger [negaLucas numbers][lucas-number] cannot be safely represented in [double-precision floating-point format][ieee754]. By default, the function returns an iterator which generates all `77` numbers. To limit the number of iterations, set the `iter` option.

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

var v = it.next().value;
// returns 2

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 iterNegaLucasSeq = require( '@stdlib/math/iter/sequences/negalucas' );

// Create an iterator:
var it = iterNegaLucasSeq();

// 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="links">

[lucas-number]: https://en.wikipedia.org/wiki/Lucas_number

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

</section>

<!-- /.links -->