Quickly generate a linear recurrence sequence in your browser. To get your sequence, just specify the initial values, coefficients and the length of the sequence in the options below, and this utility will generate that many linear recurrence series numbers. Created by developers from team Browserling.
Quickly generate a linear recurrence sequence in your browser. To get your sequence, just specify the initial values, coefficients and the length of the sequence in the options below, and this utility will generate that many linear recurrence series numbers. Created by developers from team Browserling.
This is an online browser-based utility for generating linear recurrence series. A linear recurrence is a recursive relation of the form xₙ = Axₙ₋₁ + Bxₙ₋₂ + Cxₙ₋₃ + Dxₙ₋₄ + Exₙ₋₅ + …. Constants A, B, C, D, E are real numbers, and xₙ is expressed in terms of the previous n elements of the series. That is, each term of the sequence is a linear function of earlier terms in the sequence. For example, the Fibonacci sequence is a linear recurrence series. It is given by the linear equation xₙ = Axₙ₋₁ + Bxₙ₋₂, where A = B = 1 (all other coefficients C = D = E = 0), with initial values x₁ = 0 and x₂ = 1. Substituting the initial values into the recurrent formula, you can find the series that forms the Fibonacci numbers. Other examples of linear recurrence equations are the Lucas numbers, Pell numbers, and Padovan numbers. In this tool, you can generate a linear recurrence with up to five terms in the sum. To specify the recurrence relation, you only need to adjust the coefficients A, B, C, D, E. If any coefficient is not specified, then this term is not used in the recurrence formula. To specify the starting values, you need to fill in the xₙ fields. You can also specify how many terms of recurrence equation you need and what symbol you want to separate them with. That's numberwang!
This is an online browser-based utility for generating linear recurrence series. A linear recurrence is a recursive relation of the form xₙ = Axₙ₋₁ + Bxₙ₋₂ + Cxₙ₋₃ + Dxₙ₋₄ + Exₙ₋₅ + …. Constants A, B, C, D, E are real numbers, and xₙ is expressed in terms of the previous n elements of the series. That is, each term of the sequence is a linear function of earlier terms in the sequence. For example, the Fibonacci sequence is a linear recurrence series. It is given by the linear equation xₙ = Axₙ₋₁ + Bxₙ₋₂, where A = B = 1 (all other coefficients C = D = E = 0), with initial values x₁ = 0 and x₂ = 1. Substituting the initial values into the recurrent formula, you can find the series that forms the Fibonacci numbers. Other examples of linear recurrence equations are the Lucas numbers, Pell numbers, and Padovan numbers. In this tool, you can generate a linear recurrence with up to five terms in the sum. To specify the recurrence relation, you only need to adjust the coefficients A, B, C, D, E. If any coefficient is not specified, then this term is not used in the recurrence formula. To specify the starting values, you need to fill in the xₙ fields. You can also specify how many terms of recurrence equation you need and what symbol you want to separate them with. That's numberwang!
In this example, we generate a second-order linear recurrence relation. We set A = 1, B = 1, and specify initial values equal to 0 and 1. From these conditions, we can write the following relation xₙ = xₙ₋₁ + xₙ₋₂. This relation is a well-known formula for finding the numbers of the Fibonacci series.
In this example, we're using the same linear recurrence as in the previous example because A = B = 1. However, here the first initial value is 2 and the second is 1. So, we get the recursion xₙ = xₙ₋₁ + xₙ₋₂, with x₁ = 2, x₂ = 1. These conditions correspond to the recurrence formula that calculates the Lucas number sequence.
In this example, we calculate a third-order linear recurrence equation. It has the following coefficients: A = 0, B = 1, C = 1, and initial values: x₁ = 1, x₂ = 1, x₃ = 1. So, we get the linear equation xₙ = xₙ₋₂ + xₙ₋₃, which forms the Padovan sequence. We calculate the following numbers up to x₂₀ term and separate them with a semicolon character.
In this example, we generate Pell numbers. Pell numbers are calculated by the following recurrence: xₙ = 2xₙ₋₁ + xₙ₋₂, where x₁ = 0, x₂ = 1. That is, a doubled previous term plus another previous term forms the next term. For example, 2*1 + 0 = 2, 2*2 + 1 = 5, 2*5 + 2 = 12, and so on. We generate twelve Pell numbers, and place "=>" symbol between them.
In this example, we calculate the Pell-Lucas series (also known as companion Pell series). Pell-Lucas numbers are calculated according to the same recurrence formula as in the previous example, but here both initial values are equal to 2. As the initial values are even, and the equation is linear and has no odd terms, the Pell-Lucas numbers are always even.
In this example, we generate Perrin numbers. The linear relation for the Perrin series is the same as for the Padovan series (see example above) but with different initial conditions – x₁ = 3, x₂ = 0, x₃ = 2. We calculate forty Perrin numbers and separate them by the "~" character.
In this example, we set one coefficient to a negative value and get the following recurrence formula xₙ = xₙ₋₂ - xₙ₋₁. This means that the next series member is calculated as the difference between the two previous ones. We use the initial values 0 and 1 for the first two terms, and here's how we calculate some of following terms: 0 - 1 = -1, 1 - (-1) = 2, -1 - 2 = -3, and so on. As you can see, these numbers are members of the Negafibonacci sequence. We find 15 elements and separate them with a comma character.
In this example, the recurrence relation is very similar to the previous example, but here we set the coefficient B = -1, and the first two values both to 1. Let's try to calculate a few subsequent values. F₃ = 1 - 1 = 0, F₄ = 0 - 1 = -1, F₅ = -1 - 0 = -1, F₆ = -1 - (-1) = 0, F₇ = 0 - (-1) = 1, F₈ = 1 - 0 = 1. As you can see in terms 7 and 8, we have returned to our initial values. What that means is that the sequence will periodically repeat and we get a cycle.
In this example, we use a linear equation with five members. The number of members in the equation determines the order of the series. In this case, it's the fifth order series. From the given coefficients we get the following relation xₙ = xₙ₋₁ - xₙ₋₂ + xₙ₋₃ - xₙ₋₄ + xₙ₋₅, with initial values x₁ = x₃ = x₅ = 0.5, and x₂ = x₄ = 1. We've selected the initial conditions so that the series is periodic. That is, after every 6 terms the result repeats again. We generate 100 numbers here and separate them with a space.
You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!
Create a list of numberwang numbers.
Create a list of neat looking numbers.
Visualize a number by drawing its digits as a color gradient.
Create a matrix of numbers with rows and cols having same sum.
Given numbers and a grammar, recursively rewrite them.
Create a number from the mantissa, base, and exponent.
Show how a fp number is represented in a computer.
Convert a number to the a×10<sup>b</sup> form.
Convert a number in scientific notation to a regular number.
Create a list of unary numbers (1, 11, 111, 1111, …).
Create a list of alphabetic numbers (a, b, c, …, z, aa, ab, …).
Create a list of Roman numbers (i, ii, iii, iv, v…).
Create a list of Braille numbers (⠂, ⠆, ⠒, ⠲, ⠢, …).
Create a list of random binary numbers.
Create a list of random octal numbers.
Create a list of random decimal numbers.
Create a list of random hexadecimal numbers.
Calculate a cumulative sum of a list of numbers.
Calculate a cumulative difference of a list of numbers.
Calculate a cumulative product of a list of numbers.
Divide two numbers and find their quotient.
Divide the digits of the given number.
Find the factorial of a number.
Find the average of multiple numbers.
Find the mean of multiple numbers.
Find the mode of multiple numbers.
Create one or more anagrams of a number.
Create a list of digit bigrams from a number.
Create a list of digit trigrams from a number.
Create a list of digit ngrams from a number.
Create a list of polynomial progression numbers.
Create a list of metric prefixes.
Report how many digits appear how many times.
Convert a cardinal number to an ordinal number.
Convert an ordinal number to a cardinal number.
Convert Arabic numerals to Roman numerals.
Convert Roman Numerals to Arabic numerals.
Calculate a series of extended Fibonacci numbers.
Find numbers that are both Fibonacci numbers and primes.
Check if a number is a Fibonacci number.
Check if a number is both a Fibonacci number and a prime.
Create a sequence of Fibonacci words.
Create a sequence of Tribonacci words.
Create a sequence of Tetranacci words.
Create a sequence of Pentanacci words.
Calculate a series of extended Lucas numbers.
Calculate a series of extended Lucas numbers.
Check if a number is both a Lucas number and a prime.
Calculate a sequence of Moser-Bruijn numbers.
Calculate a sequence of Oldenburger-Kolakoski numbers.
Calculate a sequence of Stanley numbers.
Calculate a sequence of self-describing Gijswijt numbers.
Calculate a sequence of Rusin-Shapiro numbers.
Calculate a sequence of Baum-Sweet numbers.
Calculate members of Thue-Morse number series.
Create a list of perfect numbers.
Create a list of almost perfect numbers.
Calculate a sequence of abundant numbers.
Calculate a sequence of deficient numbers.
Generate a list of paperfolding sequence numbers.
Create a list of numbers that are not prime.
Generate an LCD display that shows the given number.
Generate a table of numbers.
Check if the given number is a perfect number.
Check if the given number is an abundant number.
Check if the given number is a deficient number.
Find the modulus of a number.
Group together digits of a number.
Create a list of digits from a number.
Apply sprintf or printf function to numbers.
Let Zalgo destroy your numbers.
Repeat a number multiple times.
Create a mirror copy of a number.
Add zeros to a number.
Add a padding of custom symbols to a number.
Reverse the order of digits of a number.
Cyclically rotate digits of a number to the left or right.
Add one to the given number.
Add one to every digit in a number.
Subtract one from the given number.
Subtract one from every digit in a number.
Discover patterns in sequences of numbers.
Find how often numeric values occur.
Find x% of a number.
Create numbers of arbitrary length and properties.
Print the Googol/Google number, which is 10<sup>100</sup>.
Print the biggest number in the world.
Create a list of big numbers.
Print the smallest number in the world.
Create a list of small numbers.
Create a list of natural numbers.
Create a list of rational numbers.
Create a series of numbers where all terms are the same.
Create a sequence of real numbers.
Create a list of complex numbers.
Create a sequence of binary numbers.
Create a sequence of number pairs.
Create a sequence of number triples.
Create a sequence of number n-tuples.
Create a number with not that many digits.
Create a number with many digits.
Interweave two or more number digit-by-digit.
Rewrite a number in the decimal representation.
Convert a fraction to a decimal number.
Convert a decimal number to a fraction.
Convert a base two number to base eight number.
Convert a base two number to base ten number.
Convert a base two number to base sixteen number.
Convert a base eight number to base two number.
Convert a base eight number to base ten number.
Convert a base eight number to base sixteen number.
Convert a base ten number to base two number.
Convert a base ten number to base eight number.
Convert a base ten number to base sixteen number.
Convert a base sixteen number to base two number.
Convert a base sixteen number to base eight number.
Convert a base sixteen number to base ten number.
Convert any number in any base to any other base.
Change the significand of a number.
Change the power of a number.
Replace digits in a number with alphabet letters.
Form a spiral from the digits of a number.
Form a circle from the digits of a number.
Form a tree from the given numbers.
Form a tree from the digits of a number.
Remove the decimal separator from a decimal number.
Modify numbers so they are almost the same but have errors.
Generate various number typos.
Write numbers in a different font.
Write numbers in a bold font.
Write numbers with an underline below them.
Write numbers with a strikethrough on them.
Write numbers in a superscript font.
Write numbers in a subscript font.
Change digits in a number to Unicode look-alikes.
Change the given numbers a little bit.
Change the digits of the given numbers a little bit.
Calculate the complexity (entropy) of a number.
Test if the given number is numberwang.
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We're Browserling — a friendly and fun cross-browser testing company powered by alien technology. At Browserling we love to make peoples' lives easier, so we created this collection of number crunching tools. Our tools have the simplest user interface that doesn't require advanced computer skills and they are used by millions of people every month. Our number tools are actually powered by our web developer tools that we created over the last couple of years. Check them out!
