I changed the 13 in the Fibonacci sequence to 14 just to see what it would do.

It added the term "quotient(u_{n-1} , n)" to the Fibonacci recursion, and claimed the resulting formula fit the data perfectly.

What?

EDIT: since people seem to be confused about why this is wrong... according to the graph, the sequence starts at n = 0. So the modified Fibonacci sequence I created is:

  n | 0 1 2 3 4 5 6
  u | 1 1 2 3 5 8 14

The computer says this formula fits it perfectly:

  u[n] = u[n-1] + u[n-2] + u[n-1]/n

Let n = 5:

  8 = 5 + 3 + 5/5
  8 = 9

EDIT 2: hmm, contrary to the graph, the engine seems to assume the sequence starts at 1. So then we have

  n | 1 2 3 4 5 6 7
  u | 1 1 2 3 5 8 14

I guess the formula works if "quotient" is defined as integer division?