I emailed a Mathematician who started a relatively successful website devoted to Math and Integers about this, and this was his reply. I am not sure if this explains my original question, as Pascal's Triangle would account for the P factor in the gap, but the P is only one part of the...
I'm a little lost when it comes to the binomial coefficients. But there are also some other interesting characteristics of the gap term. The sum of the even numbers (x^2+x) and the partial sums of the octahedral numbers also shows up as factors in sequence...
Professional Help Needed--Elementary Number Theory
I will preface this by saying that I have no formal training in Mathematics. I've taken Calc 1 and a couple of Symbolic Logic classes. Forgive me if I butchered any terminology. However, this has been bugging me for a while, and I would like...