I am a physics student and had an interesting problem that I have solved, but I don't know how to proceed from here, I have some things mixed up.
I have derived the following condition:
n[i]=3*n[i+1]+7*n[i+2]+11*n[i+3]+15*n[i+4]+19*n[i+5]+23*n[i+6] +... etc. until maximum i.
for all n[i] this condition has to be satisfied.
I want to have a function that gives n[i] given the maximum i. So say I know that i-max is 10 I want to be able to derive all n[i].
The only thing I could think of was to start from maximum i and give it value 1 and then calculate (maximum i - 1) then (maximum i - 2) etcetera. The number you substract from the maximum i I will denote with k. The result is the same for each maximum i: