You are quite right when you think about 3 attacks, just miscalculating the bonuses
First main hand attack: Long sword(+6 BAB +3 STR bonus -2 Two weapon penalty =) +7
Firs Off hand attack: Short sword (+6 BAB +3 STR bonus +1 Light weapon Training -2 Two weapon penalty =) +8
Second main hand attack: Long sword(+1 BAB +3 STR bonus -2 Two weapon penalty =) +2
Why is this way? Wieldin two weapons(or a double weapon) allows you to make only one attack per round with your off-hand weapon and if your off-hand weapon is light your penalty are less than the ones you get with a non-light weapon.
Further more, the extra attack is gained at the highest attack bonus that you have, +6 in this example
Naturally, you can choose to revert the order of the two first attacks, making the sequence: First off hand attack +8, First main hand attack +7, Second main hand attack +2.
Hope this helps^^