The game of Quod

[Joshua Zucker]

In Ian Stewart's latest book, he mentions the game of Quod. (Ch 7 of
_How To Cut A Cake: and other mathematical conundrums_)

One sequence of relevance to this game is the number of squares in an
nxn board with the four corners deleted.  He says that Denis Borris
found that there are (n^4 - n^2 - 48n + 84)/12 of them, which is not
in OEIS.

He also says that Ken Duisenberg found the formula for the mxn case
(which would make a nice triangle for OEIS) but he doesn't give the
formula, nor a reference.  Anyone have a suggestion?

--Joshua Zucker