[seqfan] Alternating Vertical and Horizontal Moves In Grid

[Leroy Quet]

There is probably a really easily found solution to my question, but I will risk looking dumb, and will post this message anyway.

Is this sequence already in the EIS?

Start with an n-by-n grid. Move from square to adjacent square by moving vertically then horizontally then vertically then horizontally, following each horizontal move with a vertical move, and following each vertical move with a horizontal move.
No square may be visited more than once.

a(n) = the maximum number of squares visitable in this way on an n-by-n grid.

A variation: You must start in a corner square.

(It does not matter if the first move is vertical or horizontal, as far as the values of each a(n) are concerned, of course.)

Thanks,
Leroy Quet