Devise a proof for observation 2. If you aren't, this might be helpful. Based upon that information, you can devise an expression using both the row's seed value and the value of the previous cell to determines the cell's value.
Spreadsheets expedite the testing of conjectures.
Say a student suspects that some checkerboard-like pattern of n cells is magical. If the sum is the magic constant, he or she can then reselect the cell and drag the mouse so that many other cells are selected and use the Edit Fill command to obtain the values of the same shaped groups of cells on the square which are in the same positions relative to the initial group of cells as the cells just filled are relative to the initial off-square cell. One caution in this is that some of the new groups evaluated may include empty cells, but students would probably recognize this if it occurred. References Olivastro, Dominic. 1993. Classic Brainteasers and Other Timeless Mathematical Games of the Last 10 Centuries.