Help me accelerate linear recurrence relation!
MATL, 8 7 bytes
-1 byte thanks to @LuisMendo
Xy4LY)i

Takes the coefficients in reverse order
Try it online!
Explanation
Xy4LY)i
Xy        : Create an identity matrix of size equal to input
  4LY)    : Remove the first row
      i   : Insert input onto the stack