123, \perm{12}{12} & 1 & 1, 3, 14, 70, 288, 822, 1260, \ensuremath{\cdots} & {\rm new} \\
\hline
123, \perm{12}{21} & 3 & 1, 3, 6, 6, 0, 0, 0, \ensuremath{\cdots} &  \\
\hline
132, \perm{12}{12} & 2 & 1, 3, 11, 41, 153, 573, 2157, \ensuremath{\cdots} & \seqnum{A281593}? \\
\hline
132, \perm{12}{21} & 6 & 1, 3, 11, 43, 173, 707, 2917, \ensuremath{\cdots} & \seqnum{A026671}? \\
\hline
231, \perm{12}{12} & 2 & 1, 3, 9, 26, 72, 192, 496, \ensuremath{\cdots} & \seqnum{A072863}? \\
\hline
231, \perm{12}{21} & 4 & 1, 3, 11, 44, 186, 818, 3706, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{21}{12} & 2 & 1, 3, 12, 55, 273, 1428, 7752, \ensuremath{\cdots} & \seqnum{A001764}? \\
\hline
321, \perm{12}{12} & 1 & 1, 3, 2, 0, 0, 0, 0, \ensuremath{\cdots} &  \\
\hline
321, \perm{12}{21} & 3 & 1, 3, 11, 47, 221, 1113, 5903, \ensuremath{\cdots} & \seqnum{A217216}? \\
\hline
