time-to-botec

README.md (6098B)

---

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 # iterSquaredTriangularSeq
 
 > Create an iterator which generates a sequence of [squared triangular numbers][oeis-a000537].
 
 <!-- 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 [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>
 
 <!-- /.intro -->
 
 <!-- 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>
 
 <!-- /.notes -->
 
 <!-- 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 -->
 
 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
 <section class="references">
 
 </section>
 
 <!-- /.references -->
 
 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
 <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 -->