This challenge is about recursion (Cops' thread)
Python 3, 65 bytes (Safe)



f=lambda n,a=3,b=0,c=6,d=6:n*[1]and[a+b]+f(n-1,c,d,2*c+d,2*a+3*b)


Try it online!

Another try in Python.

The sequence is "the number of ways to fill a 2-by-n board with dominoes in three colors, so that no two same-colored dominoes touch each other". Not on OEIS.



Let's say n=6. The board looks like:

######
######

and these are valid domino tilings in three colors (1-3 represent a color each):

123123 122331 212332 212121 113311
123123 133221 212112 212121 331133

but these are not (two same-colored dominoes are touching each other):

112323 332333 211113
112323 112311 233223

The sequence counts all possible domino tilings that satisfy the rules for each n.



Intended solution, 58 bytes



n=int(input());a=3;b=12
for _ in[0]*n:print(a);a,b=b,a*4+b


Try it online!

Unfortunately it looks like no one bothered to simplify the recurrence relation, which was clearly shown in the recursive code. Making a program with the given double recurrence as-is doesn't work since it's Python 3.