OK, post, spoilerised, you suggested key to the pattern.

[spoiler]f(n)=f(n-1)*f(n-3) - f(n-2); for f(1)=3, f(2)=4, f(3)=5[/spoiler]

[spoiler]
f(n)=f(n-1)*f(n-2) - f(n-1) - f(n-2)
[/spoiler]

Ok, here is the way that I derived the sequence. axn1 has the correct sequence, but my formula is simpler.

[spoiler]n[sub]1[/sub]=3, n[sub]2[/sub]=4
n[sub]x[/sub] = (n[sub]x-1[/sub]*n[sub]x-2[/sub]) - (n[sub]x-1[/sub]+n[sub]x-2[/sub])[/spoiler]

[QUOTE=Uncwilly]Ok, here is the way that I derived the sequence. axn1 has the correct sequence, but my formula is simpler.[/QUOTE]

Do you really think so?
[spoiler]The only difference is that your expression adds two pairs of parentheses. I don't see how that counts as simpler.[/spoiler]

something else about this sequence:

[spoiler] Each term is the largest number that cannot be composed by a linear combination of a non-negative number[/spoiler]
[spoiler] of each of the previous two terms (holds at least until 11 39 379)[/spoiler]

[spoiler]I figured this part out back in middle school after a question at the MathCounts countdown [/spoiler]
[spoiler] was what is the largest number that cannot be created by adding 3s and 4s. [/spoiler]

also, could an admin please erase my post above this as the spoiler seems to have made my message on one line only