let k = 3
let list = [|7; 18; 6; 10; 12; 128|] 
printfn "%A" list
 
let mutable cache = Map.empty
 
for i in list.Length - 1 .. -1 .. 0 do
    if i >= list.Length - k - 1 then
        cache <- cache.Add(i, (list.[i], [i]))
    else
        let mutable maxSum = System.Int32.MinValue
        let mutable maxList = List.empty
        for j in k .. min (2*k) (list.Length - i - 1) do
            let tSum, tList = cache.[i + j]
            if tSum > maxSum then
                maxSum <- tSum
                maxList <- tList
        cache <- cache.Add(i, (list.[i] + maxSum, i :: maxList))
 
let mutable maxSum = System.Int32.MinValue
let mutable maxList = List.empty
for j in 0 .. k do
    let tSum, tList = cache.[j]
    if tSum > maxSum then
        maxSum <- tSum
        maxList <- tList
printfn "%i: %A" maxSum maxList

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