Pascal's Fibonacci Triangle
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!