The third number is not a count of samples.

In J:a:b the first number is the width of a notional region — always four — and the second is how many chroma samples the top row of it gets. The third is not the bottom row's count. It is the number of chroma samples that change between the top row and the bottom one. So 4:2:0 does not mean “no blue” and it does not mean the bottom row is empty: it means the bottom row has none of its own and shares the row above. The usual reading is everywhere, and it cannot explain 4:4:0 at all.

The engine is free and needs no account. Write the raster and the steps, and every scheme comes back as the chroma raster it actually has — 4:2:0 at HD is 960×540, so a quarter of the pixels carry all the colour, and a key cut from that is a quarter-resolution matte upsampled. It counts what each step throws away, tells a step that loses chroma from one that merely trades one axis for the other, and shows that 4:1:1 and 4:2:0 cost exactly the same 1.5 samples per pixel and are completely different pictures. Every lane ships a worked example that costs nothing. Writing the report needs credits.