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[random mural]

it's more or less manual i think

we start with 1 1 0 0 1 0 0

we can "stretch" the middle 1 to the right

1 0 2 0 1 0 0 
1 0 1 2 1 0 0```

and the right one is the same

that's 4 ways where you stretch those 2 ones

then there's 2 ways where you overstretch the middle

1 0 1 1 2 2 0
1 0 1 1 2 1 2

like, if you touched the right, there's now one more space for the middle