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Fibonacci-like Series Calculator

World's Simplest Number Tool

Quickly generate Fibonacci-like sequence in your browser. To get your series, just specify the two initial values and number of elements in the series in the options below, and this utility will generate that many Fibonacci-like numbers. Created by developers from team Browserling.

᠎᠎᠎          Tool Options

Initial Values and Series Length

First element of the series.
Second element of the series.
Series length.

Recurrence Method

Each subsequent value is
calculated as the sum of
two previous ones.
Each subsequent value is
calculated as the difference
of two previous ones.

Separator and Sign

Separate numbers with this
symbol. (By default a newline.)
Flip the sign of every
second term to the
opposite.
Alternate sign option changes
the sign starting from the
third series element.

What Is a Fibonacci-like Series Calculator?

This is an online browser-based utility for generating Fibonacci-like sequence with your own first two initial values. In the real Fibonacci sequence, the first two values are 1 and 1, and the next value is obtained by adding them 1 + 1 = 2. Then using this new value the next one is calculated as 2 + 1 = 3, and so on. Similarly, in the Lucas series, the first two values are 2 and 1, and the next one is 2 + 1 = 3. With this tool, you can create your own Fibonacci and Lucas-like series. By default, this tool will calculate an increasing sequence, however in the options above you can also choose a decreasing sequence. In this case, each next value will be calculated as the difference between the two previous ones. For example, the Negafibonacci is a decreasing sequence, and calculates as following: 0 - 1 = -1, then 1 - (-1) = 2, then (-1) - 2 = -3, and so on. The first two values of the series can be positive, negative, or even fractions. You can also specify how many numbers to calculate and what symbol to use to separate them. To make things more interesting, we've added an interesting option, which generates an alternating series by changing the sign of every second term to the opposite. That's numberwang!


Fibonacci-like Series Calculator Examples

Click to try!

Fibonacci Series

In this example, we set the initial values to 0 and 1. All the following numbers are calculated as the sum of the two previous ones. Such initial conditions correspond to the original Fibonacci sequence.

0 1 1 2 3 5 8 13 21 34
Required options
These options will be used automatically if you select this example.
First element of the series.
Second element of the series.
Series length.
Each subsequent value is
calculated as the sum of
two previous ones.
Separate numbers with this
symbol. (By default a newline.)
Flip the sign of every
second term to the
opposite.

Lucas Series

In this example, the first value is 2 and the second is 1. The third value is calculated as their sum, that is, 1 + 2 = 3, the fourth one equals 1 + 3 = 4, and so on. Thus, we get the values corresponding to the numbers in the Lucas sequence. We compute twenty such values and separate them with the comma symbol.

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349
Required options
These options will be used automatically if you select this example.
First element of the series.
Second element of the series.
Series length.
Each subsequent value is
calculated as the sum of
two previous ones.
Separate numbers with this
symbol. (By default a newline.)
Flip the sign of every
second term to the
opposite.

Negafibonacci Series

In this example, each number of the sequence is equal to the difference between the two previous ones. We start with values 0 and 1 as initial values and then to find the following element, we subtract the second one from the first one: 0 - 1 = -1. Then we use this value to calculate another element 1 - (-1) = 2, and another one (-1) - 2 = -3. As you can see, all thirty calculated values corresponding to the elements of the Negafibonacci sequence.

0; 1; -1; 2; -3; 5; -8; 13; -21; 34; -55; 89; -144; 233; -377; 610; -987; 1597; -2584; 4181; -6765; 10946; -17711; 28657; -46368; 75025; -121393; 196418; -317811; 514229
Required options
These options will be used automatically if you select this example.
First element of the series.
Second element of the series.
Series length.
Each subsequent value is
calculated as the difference
of two previous ones.
Separate numbers with this
symbol. (By default a newline.)
Flip the sign of every
second term to the
opposite.

Series with an Alternating Sign

In this example, we generate a sequence with an alternating sign. As the first two values are fractional (2.5 and 22.25), most of the following elements of the sequence are fractional too. The "Alternating Sign" option flips the sign of every second term, starting from the third value.

2.5 22.25 -24.75 47 -71.75 118.75 -190.5 309.25 -499.75 809
Required options
These options will be used automatically if you select this example.
First element of the series.
Second element of the series.
Series length.
Each subsequent value is
calculated as the sum of
two previous ones.
Separate numbers with this
symbol. (By default a newline.)
Flip the sign of every
second term to the
opposite.

Pro tips Master online number tools

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!

https://onlinetools.com/number/generate-fibonacci-like-series?first-value=0&second-value=1&count=10&separator=%255Cn&increasing-sequence=true&alternate-sign=false

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