cp's OEIS Frontend

A328340 Number of geometrically distinct symmetric open knight's tours on a 4 X (2n-1) chessboard.

%I A328340 #14 Oct 13 2019 23:02:58
%S A328340 0,2,3,17,112,620,2821,13805,69036,327978,1540792,7274254,34083946,
%T A328340 158284977,732296355,3377163866,15513066609,71017218563,324217343701,
%U A328340 1476439351581,6707726917103,30409720266127,137599767926968,621531352302268,2802892252591572,12621236296192889
%N A328340 Number of geometrically distinct symmetric open knight's tours on a 4 X (2n-1) chessboard.
%C A328340 Symmetric tours are only possible on boards of odd length. The only symmetry is a rotation by 180 degrees which results in the reversal of the tour.
%H A328340 Andrew Howroyd, <a href="/A328340/b328340.txt">Table of n, a(n) for n = 1..250</a>
%H A328340 George Jellis, <a href="http://www.mayhematics.com/t/oc.htm">Knight's tours of Four Rank Boards</a>
%e A328340 a(2) = 2 because there are 2 symmetric 4 X 3 tours:
%e A328340   +----+----+----+----+   +----+----+----+----+
%e A328340   |  8 | 11 |  6 |  3 |   |  1 |  4 |  7 | 10 |
%e A328340   +----+----+----+----+   +----+----+----+----+
%e A328340   |  1 |  4 |  9 | 12 |   |  8 | 11 |  2 |  5 |
%e A328340   +----+----+----+----+   +----+----+----+----+
%e A328340   | 10 |  7 |  2 |  5 |   |  3 |  6 |  9 | 12 |
%e A328340   +----+----+----+----+   +----+----+----+----+
%Y A328340 Cf. A079137, A328341.
%K A328340 nonn
%O A328340 1,2
%A A328340 _Andrew Howroyd_, Oct 12 2019