What was Macbeth's motive for having Banquo murdered?

The Weird Sisters' predictions regarding Macbeth said, in part, that he would become king; however, they told Banquo that he would father kings. Thus, once Macbeth does take the throne, it occurs to him that he will not pass it on to his own children but to Banquo's instead, and he finds this to be very upsetting. He now says,

They hailed him father to a line of kings.Upon my head they placed a...

The Weird Sisters' predictions regarding Macbeth said, in part, that he would become king; however, they told Banquo that he would father kings. Thus, once Macbeth does take the throne, it occurs to him that he will not pass it on to his own children but to Banquo's instead, and he finds this to be very upsetting. He now says,

They hailed him father to a line of kings.
Upon my head they placed a fruitless crown
And put a barren scepter in my grip,
Thence to be wrenched with an unlineal hand,
No son of mine succeeding.  If 't be so,
For Banquo's issue have I defiled my mind [...].  (3.1.65-70)

Macbeth has gone to quite a bit of trouble to become king, including defiling his soul with a terrible sin and weighing down his own conscience with the heaviness of that sin. Now, the idea that he did all this for himself only, to have the throne for so short a time, is unacceptable. He doesn't want to think that he did all of these things so that Banquo's descendants would get his throne, so he decides to have Banquo and his one living son, Fleance, killed so that they can no longer pose a threat to his monarchy.