Question 1013712
I'm guessing your example would go from 1 --> 6 --> 15 --> 28 --> 45, etc. Is this correct?  (I am using a multiplication table given by https://en.wikipedia.org/wiki/Multiplication_table, under "History")


Assuming this is true, first off, the negative slope would have to be rational (for obvious reasons). Furthermore, the rational number would probably need to be in lowest terms, as -2 and -4/2 are different here.


If we denote the starting point by r*c, and the "slope" by -a/b where a and b are relatively prime positive integers, then the second element is (r+b)(c+a). The third element is (r+2b)(c+2a). In general, the nth element is (r+(n-1)b)*(c+(n-1)a).