Calculating Revenue Received Vs Owed

I have created a model that shows me the money that I am owed each month. However, I receive the money over a 3 month period.

Using a formula I need to determine how much I actually receive in total each month, factoring in that I receive each months revenue in three equal payments over three months.

For example

Month 1 Month 2 Month 3 Month 4 Month 5 Month 6
$A $B $C $D $E $F

In month 1, I am owed $A, but this payment will be split over 3 months.

So in month 1 I collect $A/3. In month 2, I am owed $B but this payment will also be split over 3 months so in month 2 I collect ($A/3 + $B/3), etc etc. In month 3 I collect the ($C/3) + ($B/3) + (last payment of $a/3) etc etc

How do I present this in a formula so I dont have to adjust every single column manually?

I need to follow the same structre for another scenario using 18 months as well.