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Generate numbers in a kbonacci sequence (where each term is the sum of the previous k terms) with customizable k, initial terms, strategies and data types (number, bigint, etc).
Generate numbers in a kbonacci sequence (where each term is the sum of the previous k terms) with customizable k, initial terms, strategies and data types (number, bigint, etc).
Features

Convenience: Quickly create sequences of Fibonacci, Tribonacci and beyond.

Kbonacci: Generate kbonacci sequences for any
k >= 2
. If you've ever wanted to create a Dodecanacci (k = 12
) or Hectonacci (k = 100
), now you can! 
Custom Terms: Sequences can be created with custom initial terms.

Negative Indices: Sequences extend in both the positive and negative direction. Generate the 100th term just as easily as the 100th.

DataType Agnostic: Whether you need sequences with standard numbers, BigInts, or a custom type,
Nacci
has you covered. Any type can be used as long as type operations are provided (See NumericOps). 
Performance: Go beyond traditional generation methods with advanced strategies. These offer improved time and space performance for efficient access to deeper indices.
Install
Using npm:
npm install nacci
Using yarn:
yarn install nacci
Usage
Here are some examples for getting started. To experiment, try (JSFiddle).
Fibonacci
Create a standard Fibonacci sequence
const { Fibonacci } = require("nacci"); const fib = new Fibonacci(); // Get the 10th term console.log(fib.get(10)); // = 55
BigFibonacci
Create a Fibonacci sequence with bigints
const { BigFibonacci } = require("nacci"); const bigFib = new BigFibonacci(); // Get the 256th term console.log(bigFib.get(256n)); // = 141,693,817,714,056,513,234,709,965,875,411,919,657,707,794,958,199,867n
Negative terms
const { Fibonacci } = require("nacci"); const fib = new Fibonacci(); // Get the 10th term console.log(fib.get(10)); // = 55
Custom initial terms
Create the Lucas numbers
const { Fibonacci } = require("nacci"); const lucas = new Fibonacci([2, 1]); // Get the 10th term console.log(lucas.get(10)); // = 123
Kbonacci
Create a kbonacci sequence with a given k
const { Kbonacci } = require("nacci"); // Initialize a pentanacci sequence (K = 5) const penta = new Kbonacci(5); // Get the 10th term console.log(penta.get(10)); // = 236
Create another sequence, this time with bigints and custom initial terms.
const { BigKbonacci } = require("nacci"); const bigPenta = new BigKbonacci(5, [2n, 3n, 5n, 7n, 11n]); // Get the 128th term console.log(bigPenta.get(128n)); // = 34,793,317,941,356,809,321,160,944,117,101,129,141n
Caching
Caching is enabled by default to potentially improve subsequent calls. This can be turned on or off.
const { Tribonacci } = require("nacci"); // Create with caching off const customs = [1, 2, 3]; const seq = new Tribonacci(customs, false); // Turn on caching seq.setCached(true);
Advanced Usage
For more control over your sequences. Available options are:
Custom Dodecanacci
const nacci = require("nacci"); // Set K for a dodecanacci const K = 12; // Use numbers for indices const indexOps = new nacci.ops.SafeNumOps(); // Use bigints for values const valueOps = new nacci.ops.BigOps(); // Create the encoding const encoding = new nacci.enc.RevSumEncoding(valueOps); // Create the strategy const seq = new nacci.gen.PowerGen(2, { encoding, indexOps, valueOps, }); // Get the 128th term. // The input is a number and // the output will be a bigint console.log(seq.get(128)); // = 83,872,747,739,176,371,407,337,180,779,802,816,512n
FAQ
Q: What is the range for K?
2 <= K
There is no fixed upper bound for K.
However, it is limited by 2 main factors. If large Ks are needed, it's advised to thoroughly test your use case.

K is a
number
type, so it is able to safely represent up to2^53  1
(~9.01 quadrillion); akaNumber.MAX_SAFE_INTEGER
. 
Available Memory
Encoding and generation strategies may need to store information whose size scales with K. For example, MatrixEncoding creates KxK matrices, while SumEncoding uses arrays of length K. Since the maximum value for an array's length is
2^321
(~4.29 billion), K is lowered to this limit.Depending on the environment, the amount of available memory for this information may lower K even further. For example, a quick test on my local machine encountered fatal errors ("JavaScript heap out of memory") at
K = 43,450,368
. The test ran with Node.js, heap size of ~2GB, and used Kbonacci.
Q: What is the range for indices?
There are no fixed limits for indices.
However, they are limited by 3 main factors. If large (based on distance from 0) indices are needed, it's advised to thoroughly test your use case.

The index data type
 Using safe numbers, the range is
Number.MIN_SAFE_INTEGER <= I <= Number.MAX_SAFE_INTEGER
.  Using BigInt, the range is based on BigInt's minimum and maximum values. Yes, BigInt has limits!
 Custom data types will have their own range.
 Using safe numbers, the range is

The value data type
Values can grow quickly. It is important that the data type is able to adequately represent them.
At the time of writing:
 Using safe numbers, the Fibonacci sequence can reach index
±77
. Beyond this throws an UnsafeError.  Using BigInt, the Fibonacci sequence can reach index
±1,546,639,204
. Beyond this throws a RangeError ("Maximum BigInt size exceeded").  Custom data types will have their own range.
 Using safe numbers, the Fibonacci sequence can reach index

Available memory
Encoding and generation strategies may need to store many instances of the value's data type. For example, MatrixEncoding creates KxK matrices, while SumEncoding uses arrays of length K.
Depending on the environment, the amount of available memory may be exhausted, especially for deeper indices where values are large. For example, the Fibonacci value for index
2^30
is 224,398,770 digits long and over 224MB as a string!
Q: What can I use this for?
Use cases include:

Rate Limiting: Use sequences to create rate limiting strategies such as exponential backoff.

Cryptography: Sequences with good pseudorandom properties, such as kbonacci sequences, can be used in cryptographic algorithms and for generating keys.

Modeling: The Fibonacci sequence is wellknown for appearing in natural phenomena, such as the branching of trees, the arrangement of leaves on a stem, or the fruit sprouts of a pineapple. For this and more, kbonacci sequences can be used to model complex natural growth patterns.

Financial Markets: Some traders and analysts use the Fibonacci sequence to predict stock market movements. kbonacci sequences could potentially be applied in similar financial models to predict market dynamics.

Computer Algorithms: Can be used in dynamic programming algorithms to solve specific types of problems, such as counting ways of tiling, different paths in a grid, or ways of partitioning objects.

Algorithm Analysis: Can be used to analyze the time complexity of algorithms, especially recursive algorithms. The sequence can represent the number of operations or recursive calls being made.

Queue Theory: In computing and mathematics, kbonacci sequences can be applied to problems in queue theory where arrival or service follow a pattern similar to these sequences.

Graph Theory: Can be used to calculate the number of paths between nodes in certain types of networks.

Network Design: Can be utilized in the design and analysis of network topologies, especially in distributed systems where redundancy and fault tolerance are important.

Physics and Chemistry: These sequences can model systems where each state is a sum of the previous states, such as in certain types of chain reactions or particle interactions.

Biological Systems: The study of population dynamics in biology, where the population at a certain generation can depend on several previous generations, might also find kbonacci sequences useful for modeling.

Music and Art: Kbonacci sequences can be used to create auditory and/or visual patterns and structures
Made with ❤️ by Michael Rojas
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