btw, all numbers are subnumbers, except for the second difference one (delta squared) and it is a sub n+1 - a sub 1
For any sequence of numbers A = (a1, a2, a3, …), define ΔA to be the sequence (a2- a1, a3 – a2, a4 – a3,…) whose nth term is an+1 – an. Suppose Δ2A = (1,1,1,1,...) and a19 = 0 = a92. Find a1.
If anyone can help or provide any information that would be great. I have no clue where to start. I think finite calculus makes this significantly easier.
where the term is
So if , we have the recurrence relation
When and :
Using (1) in the format
we can now create, in exactly the same way, a similar formula that gives in terms of and ; namely:
Putting and :
I have checked this all out on an Excel spreadsheet, and it does indeed give . The spreadsheet is not terribly tidy, but I attach it for your perusal.