Minimum number of recessed lights for 29x13 room
I have a basement room with almost the exact dimensions.  You walk in the basement from stairs and basement starts in almost a corner (3/4 basement) and then you walk almost the width of the house and it is about 14 feet wide.  I have 4 cans right when you get in the basement on one switch by basement door and then a square zone of 4 in the back of the room on a dual switch (dimmed and turned off and on from the first corner and then the complete other side of the room which is a small hallway) and then another zone of 4 in the front with the same dual switch set up.  

Is 12 too many in the area.  Considering that I am using 65W bulbs... no.  With all 12 on at once the basement is well lit.  If I take one bulb out from any light, there is some dead space.  Also my basement has fully drywalled white ceilings and a bright light grey for the walls.  If I had any sort of texture or darker colors then less light.

Would I have gone less?  No way.  Honestly I don't want to have to buy lamps and stuff for your basement.  I also like to be able to see things.  When it is lit, it doesn't feel like a basement at all.  Everything has a dimmer and the 12 lights are split three ways so I don't ever feel like I have extra lights either.  I could have gone 16 easy too (2 more on the back two zones).  So my answer is 12-16.

Also you have to think how the room will be used.  I have 4 at entrance which is on the most, then 4 by TV which is on the least (or if it is on it is really dim), and 4 by sitting area which is used when people are reading or doing homework.  

If you are doing this yourself both the cost and time are minimal to add extras.  An extra pot light is $20, 30 mins, plus a minor amount of time when drywalling.