We have a regular telephone keypad and we want to know the number of "valid" 7 digit phone numbers that start from any key on the keypad, and progress to the next key using the Knight's move from chess (two squares horizontally then one vertically, or two vertically then one horizontally, making an "L" shape).

"Valid" numbers may not begin with 0 or 1.

Keypad:

1 2 3 4 5 6 7 8 9 0

you make up the phone number by traversing.
say you start with 2.
you can knight move to 9 and 7.
"29" begins one combo.
from 9, you can move to 4 or 2.
"294" is part of a combo.
from 4, 3 or 9 are possible, and so on