[bash] How to produce a range with step n in bash? (generate a sequence of numbers with increments)

The way to iterate over a range in bash is

for i in {0..10}; do echo $i; done

What would be the syntax for iterating over the sequence with a step? Say, I would like to get only even number in the above example.

#!/bin/bash
for i in $(seq 1 2 10)
do
   echo "skip by 2 value $i"
done

Bash 4's brace expansion has a step feature:

for {0..10..2}; do
  ..
done

No matter if Bash 2/3 (C-style for loop, see answers above) or Bash 4, I would prefer anything over the 'seq' command.

$ seq 4
1
2
3
4

$ seq 2 5
2
3
4
5

$ seq 4 2 12
4
6
8
10
12

$ seq -w 4 2 12
04
06
08
10
12

$ seq -s, 4 2 12
4,6,8,10,12

Pure Bash, without an extra process:

for (( COUNTER=0; COUNTER<=10; COUNTER+=2 )); do
    echo $COUNTER
done