Sequence-N-X

Overview

Module used for generating sequences of indefinite length using a function with ability to reference previous elements
It produces values when needed and stores them after they were required for the first time

Installation

``
$ npm i --save sequence-n-x
`

Examples

Fibonacci numbers
`
const sq = require("sequence-n-x");
const fibonacciNumbers = sq ( (index,n)=> n(-1) + n(-2),[1,1])
console.log(fibonacciNumbers.take (10)); // 1 1 2 3 5 8 13 21 34 55
`

Triangular numbers using formula based on index
`
const triangularNumbers1 = sq((i,n) => (i * (i + 1)) / 2);
console.log(triangularNumbers1.take (5); // 0 1 3 6 10
`

Triangular numbers with calculating next element based on previous
`
const triangularNumbers1 = sq((i,n) => n(-1) + i);
console.log(triangularNumbers1.take (5); // 0 1 3 6 10
`

Range of integers starting with 0
`
console.log(sq().take(5)); // 0 1 2 3 4
`

Interface

$3

const mySequence = sq(generatorFunction, initialValues, generateAtCreation);

$3

A function that create and return element of a sequence
`
const generatorFunctionTriangular = (index , n) => n(-1)+i;
const generatorFunctionFibo = (i,n)=> n(-1)+n(-2);
`
where
index is a position in a sequence starting with 0 (similar to iterating over arrays with ar.map((x,i)=>... )
n is a function that as an argument takes index of another element relative to one that is being created and returns it's value
n(-1) is previous element, n(-2) is element before that
n should be negative integer
if -n > index then ( attempt to get element with index < 0) 0th element will be used


Note: instead of numbers other types (strings objects arrays etc) can be used as a return value
If omitted (i)=>i would be used as default, producing 0 1 2 3... sequence

###Initial values
Array of values that start a sequence and should be defined by hand. [1,1] in Fibonacci numbers
If there is a single value, it can be passed as a single value, not like an array

Default: [0]

$3

Normally new elements would be produced only when they are required, but user can specify number of elements that would be produced at the beginning
Default: 0

$3

`
mySequence.take(amount)
`
returns array containing elements from 0th to amounth
`
mySequence.slice(start,end)
`
returns array containing elements from start to end (zero based indexes)
`
mySequence.get(index)
`
returns one element of provided index

Value generation details

By default elements are generated when retrieving methods (take slice get) are called
Each element gets generated only once and then stored
`
s1.take (5)
s1.take (10) // returns 0 to 10 but produces only elements 6 to 10
`

When elements starting from specific index are needed whole range up to the last one is generated
`
s2.slice(7,10) // returns 7 to 10 but produces 0 to 10
s2.get ( 20) // produces 0 to 20
``