[рони]

Marson,
не самый оптимальный вариант ...

const maxSumm = arr => {
    if(arr.length < 2) return Math.max(...arr, 0);
    let temp = [[0, arr[1]], [arr[0], 0]],
        up = [];
    for (let i = 2; i < arr.length; i++) {
        up = [];
        temp = temp.map(ar => {
            let last = ar[ar.length - 1],
                prev = ar[ar.length - 2];
            if (last) ar.push(0);
            else if (prev) {
                up.push([...ar, 0]);
                ar.push(arr[i])
            } else ar.push(arr[i])
            return ar
        });
        temp = temp.concat(up)
    }
    temp = temp.map(a => a.reduce((a, b) => a + b));
    return Math.max(...temp);
}
alert(maxSumm([4, 10, 3, 1, 5]))