What is the name of this?

[Unity+]

Let us say there is a formula [math]ax+b[/math], and a sequence of numbers is laid out. Let us say the formula is [math]3x+1[/math].

 

4 7 10 13 16 19 22 25 28

 

Now, let us put these numbers into sets of 3 in order.

 

{4 7 10} {13 16 19} {22 25 28}

 

Then, add up the numbers in each set to get the following sequence.

 

21 48 75

 

The pattern can be describe as each number within the sequence of sets can be found with the following, where s is the size of each set.

 

where c is some number related to the formula.

 

Has this been looked into before? If so, can someone link the webpage about it?

Edited September 20, 2013 by Unity+

[imatfaal]

or 9ax + 6a + 3b with x running from 0 upwards

 

so more generally for bigger sets

 

s^2ax+sb+sa(s+1)*/2 with s running from 1 upwards

 

ie there is no fourth independent term c

[Unity+]

or 9ax + 6a + 3b with x running from 0 upwards

 

so more generally for bigger sets

 

s^2ax+sb+sa(s+1)*/2 with s running from 1 upwards

 

ie there is no fourth independent term c

Thanks for fixing the equation.

 

I guess there isn't really anything special about it. I just found it interesting.

[Acme]

Thanks for fixing the equation.

 

I guess there isn't really anything special about it. I just found it interesting.

 

As to what it is called as your title asks, it is called a sequence just as you used the term yourself. I find sequences interesting as well and some sequences, such as the sequence of Primes, are Very Special. It is up to the individual mathematician to set forward such conditions and characteristics of a given sequence that demonstrate how and/or why it is deserves to be called Special.