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 A237429 Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with exactly one axis of reflective symmetry. 2
 0, 1, 19, 1394, 281990, 377205809, 1539951848735, 44222409563201991, 3842818845468254120853, 2396657968905952750257244144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv:1402.0545 [math.CO], 2014 FORMULA a(n) = A227257(n) - A237430(n). EXAMPLE The following two cycles with n=3 are counted only once, since they are isomorphic under the full symmetry group of the square. They have a horizontal and a vertical axis respectively.  No example has a diagonal axis, since this brings other symmetries (see A063524).   o-o-o-o-o-o   o-o o-o o-o   |         |   | | | | | |   o o-o-o-o-o   o o o o o o   | |           | | | | | |   o o-o-o-o-o   o o o o o o   |         |   | | | | | |   o o-o-o-o-o   o o o o o o   | |           | | | | | |   o o-o-o o-o   o o-o o-o o   |         |   |         |   o-o-o-o-o-o   o-o-o-o-o-o CROSSREFS Cf. A209077, A227257, A237430. Sequence in context: A107673 A130037 A047910 * A177611 A051847 A217830 Adjacent sequences:  A237426 A237427 A237428 * A237430 A237431 A237432 KEYWORD nonn,walk AUTHOR Ed Wynn, Feb 07 2014 STATUS approved

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Last modified November 14 03:52 EST 2018. Contains 317159 sequences. (Running on oeis4.)