Hello, Innsmouth!

Neighbour Squares

On a standard chessboard how many different ways

. . can you select a block of five neighbour squares?

Two squares are neighbours if they have a common side.

(If the problem was asked for a 3x3 board the answer would be 49.)

I finally found the 49 ways on a 3x3 board! Code:

*-----------*
|:::::::::::|
|:::::::*---*
|:::::::| | 16 ways
*---*---* |
| |
*-----------*

Code:

*-----------*
|:::|:::|:::|
*:::*---*:::*
|:::| |:::| 8 ways
*---* *---*
| |
*-----------*

Code:

*-------*---*
|:::::::| |
*---*:::*---*
| |:::::::| 8 ways
| |:::*---*
| |:::| |
*---*---*---*

Code:

*-----------*
|:::::::::::|
|:::*-------*
|:::| | 4 ways
|:::| |
|:::| |
*---*-------*

Code:

*-----------*
|:::::::::::|
*---*:::*---*
| |:::| | 4 ways
| |:::| |
| |:::| |
*---*---*---*

Code:

*---*-------*
| |:::::::|
* |:::*---*
| |:::| | 4 ways
*---*:::| *
|:::::::| |
*---*---*---*

Code:

*---*-------*
|:::| |
|:::*---* |
|:::::::| | 4 ways
*---*:::*---*
| |:::|:::|
*---*---*---*

Code:

*---*---*---*
| |:::| |
*---*:::*---*
|:::::::::::| 1 way
*---*:::*---*
| |:::| |
*---*---*---*

On an 8x8 board, these would have many more placements.

Plus, we must place the other four "Pentominoes". Code:

*-------*
|:::::::|
*---*:::*-------*
|:::::::::::|
*-----------*
*---*
|:::|
|:::*-----------*
|:::::::::::::::|
*---------------*
*---*
|:::|
*---*:::*-------*
|:::::::::::::::|
*---------------*
*-------------------*
|:::::::::::::::::::|
*-------------------*

That's a LOT of counting!