The SEQUENCE function is a useful function in Google Sheets. It’s a powerful way to generate numbered lists.
Previously, you had to resort to obscure array formulas like
=ArrayFormula(row(1:5))to get lists of numbers. Things got ugly fast if you wanted to customize these lists.
Thankfully today, we have the SEQUENCE function.
As arguments, 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(10,5)
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))
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.
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
You could do it like this with SEQUENCE combined with QUERY:
`=ArrayFormula( QUERY(
MOD( SEQUENCE(50) ,6),
“Select Col1 Where Col1 != 0 AND Col1 != 4 “,0 ) )`
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…..