The Piggyback Sequence I made my own sequence recently (called the Piggyback sequence), and it works like this:
P(1), P(2) and P(3) = 1.
For all P(n) where n&gt;3, the sequence works like this:
P(n) = P(n-3) + P(n-2)/P(n-1)

So, continuing the sequence:
P(4) = 1 + 1/1 = 2
P(5) = 1 + 1/2 = 3/2
= 1.5
P(6) = 1 + 2/(3/2) = 7/3
= 2.33333...
P(7) = 2 + (3/2)/(7/3) = 37/14 = 2.6428571428...
P(8) = 3/2 + (7/3)/(37/14) = 529/222
= 2.3828828828...
Your task is, when given n, calculate P(n) either as a floating point number or an (im)proper fraction.
This is code-golf, so shortest code in bytes wins.
If anyone can find the name of the sequence, please edit the post accordingly.
Current leaders: MATL and Jelly (both at 15 bytes).
Python 2, 40 39 bytes.

f=lambda x:x&lt;4or.0+f(x-3)+f(x-2)/f(x-1)


Gives True instead of 1, if this isn't allowed we can have this for 42 bytes:

f=lambda x:.0+(x&lt;4or f(x-3)+f(x-2)/f(x-1))


The way it works is pretty straightforward, the only trick is using .0+ to cast the result to a float.