123, \perm{123}{123} & 1 & 1, 4, 20, 100, 410, 1224, 2232, \ensuremath{\cdots} & 123 \\
\hline
123, \perm{123}{132} & 6 & 1, 4, 20, 100, 410, 1224, 2232, \ensuremath{\cdots} & 123 \\
\hline
123, \perm{123}{231} & 6 & 1, 4, 20, 100, 410, 1224, 2232, \ensuremath{\cdots} & 123 \\
\hline
123, \perm{123}{321} & 3 & 1, 4, 20, 100, 410, 1224, 2232, \ensuremath{\cdots} & 123 \\
\hline
123, \perm{132}{213} & 6 & 1, 4, 19, 91, 358, 1005, 1601, \ensuremath{\cdots} & {\rm new} \\
\hline
123, \perm{132}{312} & 12 & 1, 4, 19, 79, 231, 407, 354, \ensuremath{\cdots} & {\rm new} \\
\hline
123, \perm{231}{312} & 2 & 1, 4, 19, 83, 262, 514, 527, \ensuremath{\cdots} & {\rm new} \\
\hline
132, \perm{123}{123} & 2 & 1, 4, 20, 100, 490, 2366, 11334, \ensuremath{\cdots} & {\rm new} \\
\hline
132, \perm{123}{132} & 6 & 1, 4, 21, 116, 646, 3596, 19981, \ensuremath{\cdots} & 132 \\
\hline
132, \perm{123}{213} & 6 & 1, 4, 20, 102, 518, 2618, 13194, \ensuremath{\cdots} & {\rm new} \\
\hline
132, \perm{123}{231} & 6 & 1, 4, 20, 100, 486, 2302, 10690, \ensuremath{\cdots} & {\rm new} \\
\hline
132, \perm{123}{312} & 6 & 1, 4, 20, 104, 544, 2846, 14880, \ensuremath{\cdots} & {\rm new} \\
\hline
132, \perm{123}{321} & 6 & 1, 4, 20, 99, 477, 2252, 10480, \ensuremath{\cdots} & {\rm new} \\
\hline
132, \perm{132}{213} & 12 & 1, 4, 21, 116, 646, 3596, 19981, \ensuremath{\cdots} & 132 \\
\hline
132, \perm{132}{312} & 12 & 1, 4, 21, 116, 646, 3596, 19981, \ensuremath{\cdots} & 132 \\
\hline
132, \perm{213}{231} & 12 & 1, 4, 20, 100, 488, 2335, 11016, \ensuremath{\cdots} & {\rm new} \\
\hline
132, \perm{231}{312} & 4 & 1, 4, 20, 105, 559, 2990, 16021, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{123}{123} & 2 & 1, 4, 20, 97, 431, 1758, 6669, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{123}{132} & 4 & 1, 4, 20, 104, 544, 2855, 15056, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{123}{213} & 4 & 1, 4, 20, 106, 573, 3127, 17173, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{123}{231} & 4 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{123}{312} & 4 & 1, 4, 20, 105, 564, 3094, 17329, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{123}{321} & 4 & 1, 4, 20, 106, 581, 3273, 18851, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{132}{123} & 4 & 1, 4, 20, 105, 564, 3092, 17289, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{132}{213} & 4 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{132}{231} & 2 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{132}{312} & 4 & 1, 4, 20, 108, 611, 3575, 21455, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{132}{321} & 4 & 1, 4, 20, 108, 607, 3504, 20638, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{213}{132} & 4 & 1, 4, 20, 109, 629, 3793, 23669, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{213}{231} & 4 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{213}{312} & 2 & 1, 4, 20, 111, 654, 4013, 25380, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{213}{321} & 4 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{231}{123} & 4 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{231}{213} & 4 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{231}{312} & 2 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{312}{132} & 4 & 1, 4, 20, 111, 659, 4102, 26435, \ensuremath{\cdots} & {\rm new} \\
\hline
231, \perm{312}{231} & 2 & 1, 4, 21, 123, 767, 4994, 33584, \ensuremath{\cdots} & 231 \\
\hline
231, \perm{321}{123} & 2 & 1, 4, 20, 112, 673, 4243, 27696, \ensuremath{\cdots} & {\rm new} \\
\hline
321, \perm{123}{123} & 1 & 1, 4, 20, 76, 108, 52, 0, \ensuremath{\cdots} &  \\
\hline
321, \perm{123}{132} & 6 & 1, 4, 20, 103, 527, 2714, 14274, \ensuremath{\cdots} & {\rm new} \\
\hline
321, \perm{123}{231} & 6 & 1, 4, 20, 110, 644, 3934, 24770, \ensuremath{\cdots} & {\rm new} \\
\hline
321, \perm{123}{321} & 3 & 1, 4, 21, 128, 850, 5956, 43235, \ensuremath{\cdots} & 321 \\
\hline
321, \perm{132}{213} & 6 & 1, 4, 20, 113, 687, 4389, 29046, \ensuremath{\cdots} & {\rm new} \\
\hline
321, \perm{132}{312} & 12 & 1, 4, 21, 128, 850, 5956, 43235, \ensuremath{\cdots} & 321 \\
\hline
321, \perm{231}{312} & 2 & 1, 4, 20, 117, 745, 5006, 34873, \ensuremath{\cdots} & {\rm new} \\
\hline
