Recurrence relation not clear

#1

plz explain sliding window recurrence formula

#2

hello @dakshi

dp[i]=dp[i-1]+dp[i-2]+dp[i-3]…dp[i-k]; // equation 1

dp[i+1]=dp[i]+dp[i-1] +dp[i-2]+dp[i-3]…dp[i-k+1]; // equation 2

adding and subtracting dp[i-k] in above equation

dp[i+1]= dp[i]+dp[i-1]+dp[i-2]+dp[i-3]…dp[i-k+1] + dp[i-k]-dp[i-k];

dp[i+1]=dp[i]+dp[i-1]+dp[i-2]+dp[i-3]…dp[i-k+1]+dp[i-k] - dp[i-k];

using equation 1 , we can write the highlighted part as dp[i]

dp[i+1]=dp[i]+dp[i]-dp[i-k];

dp[i+1]=2*dp[i]-dp[i-k];