Perl, 78 75 72 bytes

Includes +1 for n

perl -nE '$"=",";say<@{[map"{@{[map$`*($_-.5)/@z,@z=1..$_&-$_]}}",/$/..~-$_]}\\ >' <<< 8

Prints a space separated sequence of comma separated numbers (replace the final space by \n for a more readable output)

Uses a string substitution inside a string substitution.

Perl, 78 75 72 bytes

Includes +1 for n

perl -nE '$"=",";say<@{[map"{@{[map$`*($_-.5)/@z,@z=1..$_&-$_]}}",/$/..$_-1]}\\ >' <<< 8

Prints a space separated sequence of comma separated numbers (replace the final space by \n for a more readable output)

Uses a string substitution inside a string substitution.

Perl, 78 75 bytes

Includes +1 for n

perl -nE '$"=",";print<@{[map"{@{[map$`*($_-.5)/@z,@z=1..$_&-$_]}}",/$/..$_-1]}\\\n>' <<< 8

(use say instead of print if you don't mind the extra newline).

Uses a string substitution inside a string substitution.

This doesn't feel optimal at all... (assuming it is even correct)

Perl, 78 75 72 bytes

Includes +1 for n

perl -nE '$"=",";say<@{[map"{@{[map$`*($_-.5)/@z,@z=1..$_&-$_]}}",/$/..~-$_]}\\ >' <<< 8

Prints a space separated sequence of comma separated numbers (replace the final space by \n for a more readable output)

Uses a string substitution inside a string substitution.

Perl, 78 bytes

Includes +2 for lp

The input on STDIN is the sequence number, so 1 for 2 seats, 2 for 4 seats, 3 for 8 seats etc.

perl -lpe '$"="\\ ";@F=($n=@F+1,map{;"{0,$n}+$_",$n}@F)for 1..$_}for(<@F>){s/\S+/$&/gee' <<< 3

This doesn't feel optimal at all... (assuming it is even correct)

Perl, 78 75 bytes

Includes +1 for n

perl -nE '$"=",";print<@{[map"{@{[map$`*($_-.5)/@z,@z=1..$_&-$_]}}",/$/..$_-1]}\\\n>' <<< 8

(use say instead of print if you don't mind the extra newline).

Uses a string substitution inside a string substitution.

This doesn't feel optimal at all... (assuming it is even correct)