How many arrangements of the numbers 1,2,3,...,7 are there where the sum of any two adjacent numbers is odd?
+591 for this, we would have to swap between odd and even numbers for the arrangement, so
4x3x3x2x2+4x3x3x2x2+4x3x3x2x2+4x3x3x2+4x3x3+4x3=$\boxed{552}$
