You are accessing one value beyond the end of array @a. That returns undef, and thus you get the warnings.

Since addition treats undef as 0, and that is what you, just switch off the warning:

        for($i=1;$i<=$k;$i++){
            $j = $i - 1;
            no warnings 'uninitialized';
            $b[$i] = $a[$i] + $a[$j];
        }
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