Formula in Excel or Numbers to generate a series of numbers

Question

In my spreadsheet I have two numbers, start_number and nr_iterations. I'm looking for an formula that returns a series of numbers starting with start_number - 1 and nr_iterations long (each following item with the value of one lower).

So like this:

(nr_iterations, start_number) => [my_number_serie]  
(0, 1) => []  
(1, 3) => [2]  
(2, 5) => [4, 3]  
(3, 7) => [6, 5, 4]  
(4, 9) => [8, 7, 6, 5]  

Basically, start_number is also calculated, but probably is not too important:

start_number = 1 + nr_iterations*2

I'm actually interested in the SUM of this serie numbers, if that's of any help.

Answer 1

Enter the following formulae in the cells indicated:-

[A1] =ROW(A1)-1
[B1] =2*A1+1
[C1] =B1*(B1-1)/2-A1*(A1+1)/2

Then copy A1:C1 down as many rows as you need:

Notes:-

• If you want column headers and you need your data to start at a different row, then change the offset in the first cell (eg to start from row 3, A3 should be =ROW(A3)-3).
• The sum in column C is derived using the formula that the sum of the first n integers is n*(n+1)/2.
• I tested using LibreOffice, but Excel will be compatible.