The SEQUENCE function is a useful function in Google Sheets. It’s a powerful way to generate numbered lists.
=SEQUENCE(rows, columns, start, step)As arguments for the SEQUENCE function, you specify 1) the number of rows, 2) the number of columns, 3) a start value, and 4) a step size.
Arguments 2, 3, and 4 are optional. However, if you want to set them you need to include the previous ones (e.g. if you want to set a step size in argument 4, then you need to set 1, 2, and 3 as well).
Keep this order in mind as you look through the examples below and you’ll soon understand how the function works.
1. Ascending list of numbers
=SEQUENCE(5)
2. Horizontal list of numbers
Set the row count to 1 and the column count to however many numbers you want e.g. 5:
=SEQUENCE(1,5)
3. Two-dimensional array of numbers
Set both row and number values:
=SEQUENCE(5,5)
4. Start from a specific value
Set the third argument to the value you want to start from e.g. 100:
=SEQUENCE(5,1,100)
5. Use a custom step
Set the fourth argument to the size of the step you want to use, e.g. 10:
=SEQUENCE(5,1,1,10)
6. Descending numbers
Set the fourth argument to -1 to count down:
=SEQUENCE(5,1,5,-1)
7. Negative numbers
Set the start value to a negative number and/or count down with negative step:
=SEQUENCE(5,1,-1,-1)
8. Dates
Dates are stored as numbers in spreadsheets, so you can use them inside the SEQUENCE function. You need to format the column as dates:
=SEQUENCE(5,1,TODAY(),1)
9. Decimal numbers
Unfortunately you can’t set decimal counts directly inside the SEQUENCE function, so you have to combine with an Array Formula e.g.
=ArrayFormula( SEQUENCE(5,1,10,1) / 10 )
10. Constant numbers
You’re free to set the step value to 0 if you want an array of constant numbers:
11. Monthly sequences
Start with this formula in cell A1, which gives the numbers 1 to 12 in a column:
=SEQUENCE(12)In the adjacent column, use this DATE function to create the first day of each month (formula needs to be copied down all 12 rows):
=DATE(2021,A1,1)This can be turned into an Array Formula in the adjacent column, so that a single formula, in cell C1, outputs all 12 dates:
=ArrayFormula(DATE(2021,A1:A12,1))Finally, the original SEQUENCE formula can be nested in place of the range reference, using this formula in cell D1:
=ArrayFormula(DATE(2021,SEQUENCE(12),1))This single formula gives the output:
1/1/2021
2/1/2021
.
.
.
12/1/2021
It’s an elegant way to create a monthly list. It’s not dependent on any other input cells either (columns A, B, C are working columns in this example).
With this formula, you can easily change all the dates, e.g. to 2022.
Building in steps like this a great example of the Onion Method, which I advocate for complex formulas.
12. Text and Emoji sequences
You can use a clever trick to set the SEQUENCE output to a blank string using the TEXT function. Then you can append on a text value or an emoji or whatever string you want to create a text list.
For example, this repeats the name “Ben Collins” one hundred times in a column:
=ArrayFormula(TEXT(SEQUENCE(100,1,1,1),"")&"Ben Collins")And, by using the CHAR function, you can also make emoji lists. For example, here’s a 10 by 10 grid of tacos:
=ArrayFormula(TEXT(SEQUENCE(10,10,1,1),"")&CHAR(127790))
13. Lists Of Grouped Numbers
Suppose we’re organizing an event and we want to group our 20 participants into groups of 5.
Start with the standard SEQUENCE function to output a numbered list from 1 to 20:
=SEQUENCE(20)Next, divide by 5:
=SEQUENCE(20)/5This gives a single output, 0.2, so we need to wrap it with an array formula to get the full column output:
=ArrayFormula(SEQUENCE(20)/5)Finally, we add ROUNDUP to create the groups shown in the image above:
=ArrayFormula(ROUNDUP(SEQUENCE(20)/5))
14. Repeating Sequence
To create a repeating sequence 1,2,3,1,2,3,1,2,3,etc. use the SEQUENCE function in combination with the MOD function:
=ArrayFormula(MOD(SEQUENCE(100,1,0),3)+1)
Have you got any examples of using the SEQUENCE function?
Hi Ben!
Always loved your way of creativity. You see all possibilities in a single function.
Please see the first 50 Fibonacci numbers
=index(((1+5^(1/2))^SEQUENCE(50)-(1-5^(1/2))^SEQUENCE(50))/(2^SEQUENCE(50)*5^(1/2)))
Love it! Great work, Max!
1. Wrap the SEQUENCE in an ARRAYFORMULA(ROUNDUP & a divide operation to make multiples of each number in the list, e.g. =ARRAYFORUMLA(ROUNDUP(SEQUENCE(9,1,1)/3)) generates a column vector {1;1;1;2;2;2;3;3;3}
2. Feed a SEQUENCE starting at 65 into an ARRAYFORMULA(CHAR to create a sequence of letters (because CHAR(65)=”A”), e.g. =ARRAYFORMULA(CHAR(SEQUENCE(1,9,65))) generates a row vector {A,B,C,D,E,F,G,H,I}
3. Concatenate row & column vectors generated with SEQUENCE using ‘&’ within the ARRAYFORUMLA to generate grids containing all the possible combinations (e.g. concatenating the above two examples generates an 9×9 grid starting at 1A & ending at 3I)
Very nice! I like the row vector of letters. Thanks for sharing.
Cheers,
Ben
Hi Ben,
Could you do an article about non-linear and looping sequences?
For example I’m stuck trying trying make this simple sequence for many rows: 1,2,3,5,1,2,3,5,1,2,3,5
Hope I’m not treading on anyone’s toes here, but I’d approach it like this (e.g. for 10 loops): =ARRAYFORMULA(FLATTEN({1,2,3,5}&LEFT(A1:A10,0)))
N.B. Using 0 as the second argument of LEFT returns an empty string; within an ARRAYFORMULA empty arrays can be made this way. The column of cells referred to in the LEFT can be anywhere on the sheet; it is the number of cells in the column range that controls the number of loops.
Hi Lucas,
There are several ways of creating non-linear sequences. One method is to use Query to filter out non wanted values.
Example:
=ArrayFormula(QUERY(
MOD(SEQUENCE(50),6),
"Select Col1
Where Col1 != 0
AND Col1 != 4 ",0 )
)
Thanks, Ben! Especially for monthly sequences.
Is there any way to upgrade the formula when I want every month for example three times?
I mean
1/7/2021
1/7/2021
1/7/2021
1/8/2021
1/8/2021
1/8/2021
and so on till the end of the next year.
Thank you.
Milan
This generates a sequence of 3’s for the 12 months of the year
=ArrayFormula(“1/”&ROUNDUP(SEQUENCE(36)/3)&”/2021”)
Very nice and helpful. 🙂
HI BEN,
How can we make a list that starts with a constant, the output required :
AB-1
AB-2
AB-3
….
I tried =CONCATENATE(“AB-“,SEQUENCE(10,1,1,1))
got AB-12345678910
the only solution for me now is to make a column with sequence
and then concatenate to another column.
can you have a solution to make it in one step
=SEQUENCE(10,1,1,1) | =CONCATENATE(“AB-“,T12)
1 | AB-1
2 |AB-2
3…..
Akram wrap it with an array formula, using the TEXT function to concatenate.
=ARRAYFORMULA(TEXT(SEQUENCE(10;1;1;1);”\A\B\-0″))
=ArrayFormula(“AB-“&sequence(10))
Ben,
Is there a way to use the sequence where I have a spreadsheet with the layout below that the Column A represents the equipment ID and column B is the sequence of the orders to be ran. The first row of each pieces of equipment is empty and could house a formula but new orders are added and old ones taken out daily. I would just like to be able to sequence automatically.
Thanks
F102
F102 1
F102 2
F102 3
F104
F104 1
F104 2
F104 3
F104 4
F105
F105 1
F105 2
Trying to take the difference between two numbers which we are abbreviating as years. For example,
we enter in 50 60 in a cell. I want to have this output
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960.
First I was splitting the cell into two columns then adding 1900 to each number to change this to the correct year. We don’t care about any years in the 2000’s only the 1900s.
Was then attempting to use the sequence function to only show the years between the two values but I can’t seem to figure how to do this.
Hey Darren,
Not sure exactly what you’re trying to do, but these two sequence functions will give you that output you want:
In a column:
=SEQUENCE(10,1,1950,1)As a row:
=SEQUENCE(1,10,1950,1)Hope this helps!
Ben