What is 2006 Odyssey maintenance code A 13?

The codes can be either A or B, and sub-codes 1 through 5. You have A 1,3.

At least for a 2007 Odyssey (from the manual):

A - Replace engine oil
B - Replace engine oil and oil filter
Inspect brakes
Check parking brake
Inspect tie rods, suspension, driveshaft boots, brake lines, fluids, exhaust, and fuel lines

1 - Rotate tires
2 - Replace air cleaner element
Replace dust and pollen filter
Inspect drive belt
3 - Replace Transmission Fluid
4 - Replace spark plugs
Replace timing belt and inspect water pump
Inspect valve clearance
5 - Replace engine coolant

So, A 13 means replace engine oil and transmission fluid, and rotate the tires. Please note that this is an abbreviated listing from the manual, which has notes and exceptions on the items above. Please consult your manual or a Honda dealer for a more detailed explanation.