Pascal's Fibonacci Triangle What do you get when you cross Pascal's Triangle and the Fibonacci sequence? Well, that's what you have to find out!
Task
Create a triangle that looks like this:
          1
        1   1
       2  2  2
    3   5  5   3
  5  10  14  10  5
8  20  32  32  20  8

Basically, instead of each cell being the sum of the cells above it on the left and right, you also need to add the cell on the left above the cell on the left and the cell on the right above the cell on the right.
This is A036355.
You may choose to do one of the following:

Output the \$n\$th row (indexed as you wish)
Output the first \$n\$ rows
Output all rows infinitely

Rules

Each row may be represented as a string separated by some character that is not a digit or an ordered collection of numbers. You do not need to align the triangle like I did in the example.
If you choose to output multiple rows, you need either an ordered list of rows, or a string that uses a different separator than the one you use within rows.
Please specify which task you chose in your answer, along with the input (if applicable) and output format.
You can receive input and output through any of the standard IO methods.
This is code-golf, so shortest code in bytes wins!

Bounty
As Scala is the language of the month, I will be giving a 50 rep bounty for any Scala answers to this question (not just if you're a first-time user). If multiple Scala answers are posted, I will be happy to put a bounty on a different Scala answer of yours instead.
Python 2, 73 72 69 bytes
-1 byte thanks to dingledooper!
-3 bytes thanks to Sisyphus!
Prints the rows indefinitely.

c=a=[0]
b=[1]
while 1:print b;a,b=b,map(sum,zip(c*2+a,a+c*2,c+b,b+c))

Try it online!