For example a..b1..3 expands to a1 a2 a3 b1 b2 b3.

If I wanted to print a1 b1 c1 a2 b2 c2 a3 b3 c3, is there an analogous way to do that? What's the simplest way?

You could do:

$ eval echo 'a..c'1..3
a1 b1 c1 a2 b2 c2 a3 b3 c3

Which then tells the shell to evaluate:

echo a..c1 a..c2 a..c3

a..c1 a..c2 a..c3

The brace expansions in a..c1..3 are expanded left to right, so you first get a1..3 b1..3 c1..3 and then the letters are combined with the numbers into a1 a2 a3 b1 b2 b3 c1 c2 c3. To get the order you want, you will have to use the slightly longer expression above.

For this particular case, I think that the option given by Stéphane Chazelas is the best one.

On the other hand, when you expand more complex things, this option doesn't scale well. So, you can achieve the same with this:

printf '%s' a..c1..3 | sort -zk 1.2,1.2 | tr '' ' '

which returns:

a1 b1 c1 a2 b2 c2 a3 b3 c3

Seems a little messy, but now, I have a huge control in the order, just changing two chars in the command above; for example:

echo a..b1..2a..b1..2

this will expand to:

a1a1 a1a2 a1b1 a1b2 a2a1 a2a2 a2b1 a2b2 b1a1 b1a2 b1b1 b1b2 b2a1 b2a2 b2b1 b2b2

Suppose I want all the 1 in the second expansion, then the 2:

printf '%s' a..b1..2a..b1..2 | sort -zk 1.2,1.2 | tr '' ' '
a1a1 a1a2 a1b1 a1b2 b1a1 b1a2 b1b1 b1b2 a2a1 a2a2 a2b1 a2b2 b2a1 b2a2 b2b1 b2b2

Suppose I want all the a in the third expansion, then the b:

printf '%s' a..b1..2a..b1..2 | sort -zk 1.3,1.3 | tr '' ' '
a1a1 a1a2 a2a1 a2a2 b1a1 b1a2 b2a1 b2a2 a1b1 a1b2 a2b1 a2b2 b1b1 b1b2 b2b1 b2b2

Suppose I want all the 1 in the fourth expansion, then the 2:

printf '%s' a..b1..2a..b1..2 | sort -zk 1.4,1.4 | tr '' ' '
a1a1 a1b1 a2a1 a2b1 b1a1 b1b1 b2a1 b2b1 a1a2 a1b2 a2a2 a2b2 b1a2 b1b2 b2a2 b2b2

Suppose I want all the 1a in the middle, then 1b, then 2a, then 2b:

printf '%s' a..b1..2a..b1..2 | sort -zk 1.2,1.3 | tr '' ' '
a1a1 a1a2 b1a1 b1a2 a1b1 a1b2 b1b1 b1b2 a2a1 a2a2 b2a1 b2a2 a2b1 a2b2 b2b1 b2b2

You can even, just as easily, reverse any order in the expansions above, just adding and r to the previous command; for example, the last one:

printf '%s' a..b1..2a..b1..2 | sort -rzk 1.2,1.3 | tr '' ' '
b2b2 b2b1 a2b2 a2b1 b2a2 b2a1 a2a2 a2a1 b1b2 b1b1 a1b2 a1b1 b1a2 b1a1 a1a2 a1a1

Using a loop:

for l in a..b; do printf '%sn' "$l"1..3; done

This will loop through your first expansion and then expand each character with the second.

If you need the output all on one line you can remove the n:

for l in a..b; do printf '%s ' "$l"1..3; done

This won't give you a trailing newline but if you are passing it to a command or variable that shouldn't be an issue.

bash, ksh, zsh

A one liner that works in (bash, ksh, zsh) (not all shells can do "Brace expansion" in reverse order):

$ echo 3..1c..a | rev
a1 b1 c1 a2 b2 c2 a3 b3 c3

An alternative that use eval (which still is for bash,ksh,zsh and may be more criptic) is:

$ eval echo 'a..c'1..3
a1 b1 c1 a2 b2 c2 a3 b3 c3

To understand what happens, replace eval with echo:

$ echo echo 'a..c'1..3
echo a..c1 a..c2 a..c3

The command executed (after eval expansion) is actually echo a..c1 a..c2 a..c3. Which expands as you want/need.

all shells

For all shells, use:

$ for i in 1 2 3; do for j in a b c; do printf "%s%s " "$j" "$i"; done; done; echo
a1 b1 c1 a2 b2 c2 a3 b3 c3

If you don't mind a trailing space.

If you must have no trailing space added:

$ s=""; for i in 1 2 3; do for j in a b c; do printf "%s%s" "$s" "$j" "$i"; s=" "; done; done; echo
a1 b1 c1 a2 b2 c2 a3 b3 c3