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I understand that the total number of Knights tours is known for boards up to 8 x 8.

These are: 1, 0, 0, 0, 1728, 6637920, 165575218320, 19591828170979904

As found here: "http://oeis.org/A165134"

Could some please explain the relationship between those numbers, or how they are increasing in relation to how board size increases.

Thanks.

E. OS
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    https://math.stackexchange.com/questions/636/how-many-knights-tours-are-there may help – TomGrubb Jul 03 '17 at 23:11
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    It's not clear to me what you're asking. These numbers have no known formula, either explicit or recursive. That's why the OEIS sequence only goes up to $n=8$. It's not even obvious that they are increasing for $n > 8$. – Robert Israel Jul 03 '17 at 23:28
  • @Shailesh that one seems less general the OP talked about 64 squares ( aka 8 by 8) –  Jul 04 '17 at 02:13

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