Insert a new line after every N lines?

With awk:

awk ' {print;} NR % 2 == 0 { print ""; }' inputfile

With sed (GNU extension):

sed '0~2 a\\' inputfile

With bash:

#!/bin/bash
lines=0
while IFS= read -r line
do
    printf '%s\n' "${line}"
    ((lines++ % 2)) && echo
done < "$1"

Using paste

 paste -d'\n' - - /dev/null <file

sed n\;G <infile

... is all you need ...

For example:

seq 6 | sed n\;G

OUTPUT:

1
2

3
4

5
6

...(and a blank follows the 6 as well)...or...

seq 5 | sed n\;G

OUTPUT:

1
2

3
4

5

(and no blank follows the 5)

If a blank should always be omitted in a last line case:

sed 'n;$!G' <infile