How many different flops can there be disregarding suits

[VeryTnA]

I know there are 169 different possible pockets.
AA
AKsuited
AKoff
KK
KQsuited
KQoff
etc. etc. for a total of 169.
Forget suits, how many different 3 card flops?

[SumZero]

If you don't care about suits and you don't care about cards in people's hands (including your own) then this is pretty easy:

number of no duplicate flops + number of paired flops + number of trips flops
= 13*12*11/(3*2) + 13*12 + 13
= 13*11*2 + 13*12 + 13
= 13 * (22 + 12 + 1)
= 13 * 35
= 455

[pzhon]

There are 13 choose 3 = 286 unpaired flops.
There are 13*12 = 156 paired flops.
There are 13 flops of one rank.
Total: 286+156+13 = 455.

If you want to distinguish suitedness of the flops, but not the particular suits, you can refine these:

Each unpaired flop has 5 possible patterns (monochrome, rainbow, and 3 2-tone patterns).
Each paired flop has 2 possible patterns (two-tone or rainbow).
Each trips flop has 1 possible pattern (rainbow).
Total: 5(286)+2(156)+1(13) = 1755.

As a check, 286(4 + 24 + 3*12) + 156(12 + 12) + 13(4) = 52 choose 3.