データファイル作成

$ curl -s http://www.billboard.com/rss/charts/hot-100 | sed -n -e 's/<title>\([0-9]\+:.*\)<\/title>.*/\1/p' | head | tee billboardtop10.txt
  1: One Dance
  2: Can't Stop The Feeling!
  3: Don't Let Me Down
  4: Panda
  5: This Is What You Came For
  6: Cheap Thrills
  7: Needed Me
  8: Don't Mind
  9: Ride
  10: Work From Home

• sed

sedで偶数行を出力

$ sed -n 'n;p' billboardtop10.txt 
  2: Can't Stop The Feeling!
  4: Panda
  6: Cheap Thrills
  8: Don't Mind
  10: Work From Home

sedで奇数行を出力

$ sed -n 'p;n' billboardtop10.txt 
  1: One Dance
  3: Don't Let Me Down
  5: This Is What You Came For
  7: Needed Me
  9: Ride

• awk

awkで偶数行を出力

$ awk 'NR % 2 == 0' billboardtop10.txt 
  2: Can't Stop The Feeling!
  4: Panda
  6: Cheap Thrills
  8: Don't Mind
  10: Work From Home

awkで奇数行を出力

$ awk 'NR % 2 == 1' billboardtop10.txt 
  1: One Dance
  3: Don't Let Me Down
  5: This Is What You Came For
  7: Needed Me
  9: Ride

参考 vim で一行おきに削除

:g/^/+d
:1d|g/^/+d