A383662
Number of closed knight's tours in the first 2n cells of a 6 X ceiling(2n/6) board.
Original entry on oeis.org
6, 0, 2, 302, 8, 151, 19072, 9862, 18202, 1603948, 1067638, 1310791, 107096187, 55488142, 66608924, 6149236417, 3374967940, 4259963914, 402706752421, 239187240144, 292999006211, 26470682075988, 15360134570696, 18595568012716, 1685811256230132, 964730606632516, 1173328484648288
Offset: 11
For n=11, one of the a(11)=6 solutions is
1 4 13 16
12 15 2 5
3 22 17 14
8 11 6 19
21 18 9
10 7 20 .
- Donald E. Knuth, Hamiltonian paths and cycles, Prefascicle 8a of The Art of Computer Programming (work in progress, 2025).
- Don Knuth, Table of n, a(n) for n = 11..150
- Don Knuth, CWEB program with input parameter board,50,6,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase].
A193054
Number of closed Knight's tours on a 7 X 2n board.
Original entry on oeis.org
0, 0, 1067638, 34524432316, 1250063279938854, 38350427205194670084, 1254934986399237346242334, 40157773188600794694366079616, 1293153423896688571314211086231916, 41575689378315795601749194654016984354, 1337089200028352592236847382536061361269314
Offset: 1
A175855
The number of closed Knight's tours on a 5 X 2n board.
Original entry on oeis.org
0, 0, 8, 44202, 13311268, 4557702762, 1495135512514, 491857035772330, 161514101568508400, 53034853662012222798, 17414154188157170439208, 5717847862749642677204182, 1877435447920358266870897874, 616447390029326136628439042672, 202407848349722353779265745190616, 66459727085467788423206394162537418, 21821760546806761707309514948565417796, 7165079447164571822068029945303172129766, 2352622444655438705806553391345493395131580, 772473271844923268504474277422663237674924998
Offset: 1
The smallest 5 X 2n board admitting a closed Knight's tour is the 5 X 6, on which there are 8 such tours.
A193055
Number of closed knight's tours on an 8 X n board.
Original entry on oeis.org
0, 0, 0, 0, 44202, 55488142, 34524432316, 13267364410532, 7112881119092574, 4235482818156697040, 2122880233853945590892, 1105420672289849239070962, 586820057145837880942582376, 311550865881297158579957164664, 162703111270636640083076205067310
Offset: 1
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