Subtract the nth number from the (n+1)st. You get 2, 4, 8, 14, ? Do it again for that sequence. You get 2, 4, 6, ? Maybe that sequence is 2, 4, 6, 8, 10, 12, 14, 16, 18, ... If so, then the sequence "above" it is 2, 4, 8, 14, 22, 32, 44, 58, 74, ... And the original sequence is 2, 4, 8, 16, 30, 52, 84, 128, 186, 260, ...
Even though the mass of the sun is much greater than the mass of the moon, the moon has a greater influence on the tides than the sun. This is because the sun is much farther away from the earth, so its tidal force is only about half that of the moon.