Well, you could do this:

$worksheet1->write_col('A3', [@arr, @arr1]);
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since merging two arrays is as easy as putting them next to each other in list context (thanks to Perl's list-flattening). Alternatively, simply push the second array to the first, without taking a reference:

push @arr, @arr1;
$worksheet1->write_col('A3', \@arr);
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According to The Perl Cookbook (Recipe 4.9), the latter is more efficient. (Good book, BTW, that. I recommend it!)