Define the size n of the checkerboard to be the number of dark squares on each side of the checkerboard, and call such a checkerboard $$

The checkerboard in the picture above is $3$

Define $=$ to be the number of dark squares in $.$ As we can see in the example above, $3=13.$

Give a recursive definition of $.$ This definition must include:

All the initial conditions needed to define this sequence $($do not give more or fewer than needed$)$

A recurrence relation for $$ as a function of some of the elements of the sequence that precede $$

The values of n for which this recurrence relation applies

Explain this recursive definition. This explanation must include:

an explanation of the recurrence relation. Support this explanation with drawings of $1,2,3,4.$

an explanation of how you decided how many initial conditions were needed for this recursive definition