That assumes you can go directly from any spot to any other spot, which you can't. Given a grid that looks like this:

    123
    456
    789

you can't go directly from 1 to 3 unless 2 has been selected. I also don't think you can immediately backtrack, as in 213; you have to go 2513, for instance.

With that in mind, I wrote a quick search:

    Adjacent only (can't go from 1 to 6 or 8)
    1 9
    2 40
    3 160
    4 496
    5 1208
    6 2240
    7 2984
    8 2384
    9 784
    total: 10305
    total with length >= 4: 10096

    Non-adjacent (knight-moves) allowed (can go from 1 to 6 or 8)
    1 9
    2 56
    3 304
    4 1400
    5 5328
    6 16032
    7 35328
    8 49536
    9 32256
    total: 140249
    total with length >= 4: 139880

    Pass through previous spots, no immediate backtracking (2513 but not 213)
    1 9
    2 56
    3 304
    4 1464
    5 6136
    6 21344
    7 57184
    8 105376
    9 100928
    total: 292801
    total with length >= 4: 292432

    Pass through previous spots, with immediate backtracking allowed (213)
    1 9
    2 56
    3 320
    4 1624
    5 7152
    6 26016
    7 72912
    8 140704
    9 140704
    total: 389497
    total with length >= 4: 389112

So, I believe the correct number is 292432. For comparison, that's less secure than a 6-digit PIN, or a 4-lowercase-letter password.

More importantly, though, if you're using an unlock pattern, you can't be using disk encryption, so anyone who has physical possession of your phone need not bother brute-forcing the unlock pattern.

Pattern unlock leaves a body fat trail on the screen that is trivial NOT to see & exploit.

Exactly - if you hold my phone up to a light, you can easily see my unlock pattern in the fingerprints left on the screen.

doesn't that assume you can only select each pad once?

Yea and you can only select an adjacent spot so that also limits combinations.

You can actually select spots not adjacent to the current one.

Consider the "spots" labeled in rows from left to right as 1 2 3, 4 5 6, and 7 8 9.

If I start at 1, I can go to 2, 4, 5, 6, and 8 directly. Also, if I have used all spots except 1 and 9, I can go to 1 then directly to 9.

Yep, and the fact that the above calculation doesn't even allow for combinations greater than four... Overall not a reliable number :)

My Galaxy S4 seems to only allow one direction for each node.

You can in fact only select each pad once.