iterSquaredTriangularSeq

Create an iterator which generates a sequence of squared triangular numbers.

The squared triangular numbers are the integer sequence

$$0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, \ldots$$

starting at the 0th squared triangular number.

Triangular numbers are given by the following explicit formulas

$$T_n = \sum_{i=1}^{n} i = 1 + 2 + 3 + \ldots + n = \frac{n(n+1)}{2} = \binom{n+1}{2}$$

where the last formula corresponds to a binomial coefficient, representing the number of distinct pairs that can be selected from n+1 items.

The nth squared triangular number is the nth triangular number squared.

Usage

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

iterSquaredTriangularSeq( [options] )

Returns an iterator which generates a sequence of squared triangular numbers.

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.

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

Notes

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

Examples

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 );
}

---

See Also

• @stdlib/math/iter/sequences/triangular: create an iterator which generates a sequence of triangular numbers.