Mathematics Coursework - T Shapes

Here is a table showing the results so far for the different grid sizes, t-numbers, t-totals and the vector.

From this table I can see a pattern. It shows that when you take an Original T-total (37) and add on 5 times the vector a (3) you get the final T-total. In equation form this is:
Final T-total = Original T-total + (5xMovement in Horizontal Direction)
However this equation requires us to know the T-total In advance when we only know the T-number. So I can substitute a previous equation for the Original T-total (5n-7g). This gives me the final equation of:
Final T-total = (5n-7g)+(5a)

Therefore, I have a final formula of:
(T=Final t-total) (n=original T-number) (a=the horizontal direction on the vector)

T = (5n-7g)+5a

Testing

Prediction
Now that I have a certain formula, which has been tested, I can take any T-shape at random from any random Grid Size and use any random vector to create a final T-shape.

Justification
To prove that this formula will always work with any grid size and any T-shape using a horizontal vector I can use this T-shape, Grid and vector:

                                
                   First T-shape                                           Final T-shape