<image>Do you find mobile phones magical? They can instantly and clearly transmit sounds, texts, images, and other information. It is said that in the future they will even be able to send smell and tactile information! This is all thanks to the computer chips in mobile phones. In fact, these signals are represented in binary form in the computer chips. Each binary number is composed of 0s and 1s, with the "on" and "off" states of electronic components on the computer chip representing "1" and "0" respectively. A set of "on" and "off" states of these electronic components correspond to a binary number. For example, "on", "on", "off" represents "110".

As shown in the diagram, a segment of the circuit on a computer chip is populated with a set of electronic components (assuming they are not circularly connected), and two adjacent components cannot both be off. (The following questions require written explanations of the solving process)

(1) If there are 4 components on this circuit, how many different "on" and "off" states do these 4 components have? (Please list them one by one);
(2) Let \(a_{k}\) denote the number of different "on" and "off" states of \(k\) (\(k ≥ 1\)) components on the circuit. Try to explore the relationship between \(a_{k}\), \(a_{k+1}\), and \(a_{k+2}\) (proof not required);
(3) Using the recursive relationship explored in (2), calculate the value of \(a_{10}\).