Information on the Problem 1 2 3 4 5 6 7 8 9 10 11 12 12 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 Look at this T-Shape...
5N - 7 is correct for a grid of any size with a T-shape this way up:

Summary of work so far

So far in this investigation I have found rules to work out the T-Total when the T-Shape is on any Grid size and in any orientation from the T-Number.

The rules I have found are

Orientation of T-Shape Rule to work out T-Total from T-Number

T = 5N – 7G

T = 5N + 7G

T = 5N + 7

T = 5N – 7