Raw Input		Desired Output
Line 1 Line 2 PAT Line 3 Line 4 PAT Line 5 PAT Line 6		ODD

Raw Input		Desired Output
Line 1 Line 2 PAT Line 3 PAT

Script and Comments

Script₁ [ 1] /PAT/H [ 2] $!d [ 3] x [ 4] s/^((\n[^\n]){2})\n[^\n]*$/ODD/p [ 5] d
Comments The `-r' option of GNU sed must be used or we have to escape parentheses and braces. `Pattern Space' and `Hold Space' are abbreviated to `PS' and `HS', respectively. This script will keep every line containing PAT in the HS and count the number of lines after reading the last line. Step [1] is used to append every line containing PAT to the HS. After reading the last line, Step [3] exchanges the contents of PS and HS. Step [4] will replace the PS with `ODD' and then print it if there are odd number of lines in the PS.
Script₂ [ 1] /PAT/s/^./\n/ [ 2] /\n/H [ 3] $!d [ 4] x [ 5] s/^(\n{4})\n{2}$/ODD/p [ 6] d
Comments The previous script will consume too much memory for huge files with many lines containing `PAT'. Instead of copy entire line to the HS,this script appends to the HS a newline character `\n' each time a line containing `PAT' is read. Step [1] replaces the entire line (PS) with `\n' if it contains PAT, and the `\n' will be appended to HS in Step [2].