# Not a Fibonacci sequence

What is the next term in the sequence?

1, 1, 2, 3, 5, 8, 18, 34, 60, 120, 214, 394, 788

hints:

#1

"mapping" is a valid hint, but would probably confuse more than help

Each term is the sum of the last $$k$$ terms, but $$k$$ varies as the sequence progresses. Values of $$k$$ are: $$0,0,2,2,2,2,4,4,3,4,3,3,4$$. I am yet to determine how these values are formed. The next term is probably the sum of the last 3 terms (1396) or the last 4 terms (1516).