A247070
Number of paths joining opposite corners of an n X 3 grid with every vertex appearing at most twice in the path.
Original entry on oeis.org
3, 218, 9482, 457712, 22375458, 1103498043, 54446999831, 2687689834743, 132666417488114, 6548713810387879, 323256199668617476, 15956549284724388645, 787645179268653581373, 38879655000676000582023, 1919173045780901708089448
Offset: 1
For n = 1 corresponds to a straight line graph with vertices {1,2,3}. Then the a(1) = 3 solutions are 123, 12123, and 12323.
A247106
Number of paths joining opposite corners of an n X 4 grid with every vertex appearing at most twice in the path.
Original entry on oeis.org
5, 2100, 457712, 112269228, 28477328812, 7318410460100, 1890316186147022, 488986474759870194, 126570653719713453566, 32767699501924700122356, 8483817993681247935283336, 2196573666944370207848161336, 568727175315063817973036015946
Offset: 1
For n = 1 corresponds to a straight line graph with vertices {1,2,3,4}. Then the a(1) = 5 solutions are 1234, 121234, 123234, 123434, and 12123434.
A235389
Number of paths joining opposite corners of an n X n grid with every vertex appearing at most twice in the path.
Original entry on oeis.org
22, 9482, 112269228, 37515056726494, 355023905438833546724
Offset: 2
The 22 paths in a 2 X 2 grid whose nodes are numbered from 1 to 4 in the natural way are 124, 134, 12124, 12134, 12424, 12434, 13124, 13134, 13424, 13434, 1212434, 1213424, 1213434, 1242134, 1243124, 1243134, 1312424, 1312434, 1313424, 1342124, 1342134, 1343124. - _Giovanni Resta_, Mar 24 2014
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