Array formula offset

[argraham]

I need to summarise the total costs of building "systems" but I have variable numbers of system being built each year. Each system has a cost in year 1 as well as varying additional costs in subsequent years.

I have attempted to use array formulae but can only get the result along a single axis of an array. What I need is a solution that sums both vertically and diagonally
For example, in year 3 I build 3 new systems but must also account for the year 3 costs of the systems I built in year 1 and the systems I built in year 2.

Unfortunately, a simple manual approach is not practical as I need to scale this example up for more than 100 system summary inputs

I have attached a simplified illustrative example

Any help would be greatly appreciated