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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

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Partial answer:

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).

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    $\begingroup$ This is exactly where I'm stuck too. $\endgroup$
    – Bubbler
    Commented Mar 8, 2021 at 9:40
  • $\begingroup$ Ditto. Tried OEIS (both with and without the first two numbers) but no luck. $\endgroup$
    – Daniel
    Commented Mar 14, 2021 at 16:41

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