Consecutive Ones - State Definition

Define $dp(pos, tight, prev)$ = count of valid binary numbers from position $pos$ onward, given the previous bit was $prev$. $prev = 1$: the last placed bit was $1$.

You can only place $0$ now. $prev = 0$: the last placed bit was $0$ (or no bit yet). You can place $0$ or $1$. Base case: when $pos$ reaches the end, return $1$. You've built a valid number. This state captures all the information needed to count valid binary numbers from position pos onward.