Codeforces 455A Boredom - Transition

The transition (how we compute each state) extends the formula from unit $11$: $dp[i]$ = max(skip excitement $i$ and keep $dp[i-1]$, or take excitement $i$). If you take excitement $i$, you add $a[i]$ points but must skip $a[i]-1$ and $a[i]+1$.

That means your previous choice was from excitement $a[i]-2$ or earlier. The formula becomes $dp[i] = \max(dp[i-1], dp[i-2] + i \cdot \text{count}[i])$. You either skip value $i$ entirely, or take all copies of it (earning $i \times \text{count}[i]$) after skipping $i-1$.