Sequence and conjecture

The 4-month life-span sequence
(4MLS for short)

1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, ...

Let Sn represent the nth term in the 4MLS sequence.
Then, my conjecture is that any term where n>4, can be found using this formula
Sn = Sn-2 + Sn-3 + Sn-4.