I have a Google Sheet with the following layout:
Number | Counted? | Cumulative Total 4 | Y | 4 2 | | 6
Assuming "Number" in column A and "Counted?" in column B, try in C1
={"SUM"; ArrayFormula(if(ISBLANK(B2:B),,mmult(transpose(if(transpose(row(B2:B))>=row(B2:B), if(B2:B="Y", A2:A,0), 0)),row(B2:B)^0)))}
(Change ranges to suit).
Example